Step-by-step explanation:
The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.
To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.
The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:
x1 = 50
x2 + x3 = 100
The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:
x16 + x28 + x34 + x410 <= 480 (machining time)
x14 + x26 + x32 + x48 <= 400 (polishing time)
x14 + x24 + x34 + x46 <= 400 (assembling time)
The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:
360x1 + 240x2 + 360x3 + 480x4
The complete mathematical model for this problem is:
Maximize: 360x1 + 240x2 + 360x3 + 480x4
Subject to:
x1 = 50
x2 + x3 = 100
x16 + x28 + x34 + x410 <= 480
x14 + x26 + x32 + x48 <= 400
x14 + x24 + x34 + x46 <= 400
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.
The objective is to maximize total profit, which is given as
P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]
What is Linear Programming Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
Let[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] and [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.
The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.
These constraints can be written mathematically as:
3[tex]x_1[/tex] + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + 4[tex]x_4[/tex] ≤ 480 (Machining)
[tex]x_1[/tex] + [tex]x_2[/tex] + [tex]x_3[/tex] + 3[tex]x_4[/tex] ≤ 400 (Polishing)
2[tex]x_1[/tex] + [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + [tex]x_4[/tex] ≤ 400 (Assembling)
and, [tex]x_1[/tex] ≥ 50 (Product I)
[tex]x_2[/tex] + [tex]x_3[/tex] ≥ 100 (Products II and III)
[tex]x_4[/tex] ≤ 25 (Product IV)
[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] , [tex]x_4[/tex] ≥ 0
Learn more about Linear Programming Problem here:
https://brainly.com/question/29405467
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5. A company intends to collect a random sample of size n from a population
with population proportion of interest p. Which of the following situations would
result in the smallest standard deviation of the sampling distribution of p?
Answer:D
Step-by-step explanation:
The situations that would result in the smallest standard deviation of p is; The population proportion p ≠ 0.5, and the sample size is n.
What is the standard deviation?The formula for the standard deviation here is;
SD = √(n(p(1 - p))
Now, for the standard deviation to be maximum, it means that p = 0.5 and as such 1 - p will also be 0.5.
However, for Standard deviation to be smallest, then it means that p ≠ 0.5.
Secondly, for the sample size, it will have to remain as n and not 2n because when we say 2n, we are increasing the sample size which will in turn increase the standard deviation.
Read more about standard deviation at;
The graph of f (x) = (x - 2)² + 1 is shown below. What would the new equation of the function be if it is shifted up 2 units?
Answer:
f (x) = (x - 2)² + 3
Step-by-step explanation:
Adding 2 to the constant k would shift the entire equation upwards by 2.
Hakima and Joshua both opened savings accounts. Both started with a balance of zero dollars. For every $3 that Hakima saves in her account, Joshua saves $5. If they have saved a total of $336, how much did Hakima save?
90:(3+6)-20.(60-55) propiedad
Answer:
https://www.commoncoresheets.com/Math/Properties/Applying%20Properties%20of%20Operations/Spanish/2.pdf
Step-by-step explanation:
This will help you:) not a spam link its a pdf that brings you straight to the worksheet <3
Need the answer for x and y
Answer:
x = 7°
y = 10°
Step-by-step explanation:
7x = 49
x = 7°
180 = 13y + 1 + 49
combine like terms:
13y = 130
y = 10°
Answer:
X equals to 7 & y equals to 10 'cause ;
7X=49
X=7
50 + 13 y + 1 = 180
13y = 130
y=10
Step-by-step explanation:
Good luck.
hope it was helpful for u .
Help asap
Find the value of x. Round to the
nearest tenth.
3
4
X =
= [?]
Answer:
36.9°
Step-by-step explanation:
→ Identify the triangle required by seeing which side is not given
Hypotenuse is not given so we need to use Tan⁻¹ = Opposite / Adjacent
→ Substitute values in
Tan⁻¹ = ( 3 ÷ 4 )
→ Simplify
36.9°
Plz help NO LINKS this is due today
6(5 - 8n) + 12 = -54
please step my step
Answer:
Look Below
Step-by-step explanation:
6(5 - 8N) + 12 = -54
-48N + 30 + 12 = -54
-48N + 42 = -54
(-48N + 42) + (-42) = -54 + (-42)
-48N = -96
-48N / 48 = N
-96 / 48 = 2
N = 2
Hope This Helps! If you find any fault in my answer please let me know. Thanks! Have a good day!
5, 4, 16/5 find the 7th term
Answer:
a₇ = [tex] \frac{4096}{3125} [/tex]
help plese i beg of you
9514 1404 393
Answer:
k = 45 . . . miles per hourk = 1/45 . . . hours per mileStep-by-step explanation:
One way we can relate distance and time is ...
time = k × distance
Then the value of k (the constant of proportionality) is ...
k = time/distance = 4 hours/(180 miles)
k = (1/45) hours/mile
__
Another way we can relate the variables is ...
distance = k × time
Then the value of k (the constant of proportionality) is ...
k = distance/time = (180 miles)/(4 hours)
k = 45 miles/hour
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
for the following problems do at least one problem using unit form and at least one problem using fraction form 3.2 x 1.4=
-6x+8y=12 and -3x+4y=6
Answer:
3441
Step-by-step explanation:
PLS HOPE THIS HELP
Find the slope of the line that passes through the given points.
Answer: -1/6
Step-by-step explanation:
slope= change of y over change of x
3-4/ 5--1=
-1/6
Hope this helps!
Answer:
-1/6
Step-by-step explanation:
(-1, 4) and (5, 3)
y2 - y1 / x2 - x1
y2 = 3
y1 = 4
x2 = 5
x1 = -1
(3 - 4) / (5 - -1)
-1 / 6
slope = -1/6
Apr 08, 12:51:17 AM
Brittney wants to buy grapes and apples to bring to a party. Grapes cost $1.60
per pound and apples cost $1.75 per pound. If she only has $10 to spend on
grapes and apples, which inequality represents the situation where she buys x
pounds of grapes and y pounds of apples?
1.60x + 1.75y < 10
1.60x + 1.75y > 10
Submit Answer
1.75x + 1.60y < 10
1.75% + 1.60y > 10
Type here to search
O
12:5
4/8/
Answer: did you get a answer yet?
Step-by-step explanation:
The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.
The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.
Answer:
The quadratic equation y = -4x2 + 80x - 150 models the store's daily profit, y, for selling footballs at x dollars. you can subtract 150 from both sides and use the quadratic formula to find x=4. It can make at most 120 units in one day. 3 1. Backward Bending Supply Curve.
Round 12,628 to nearest 1,000
Answer:
13000
Step-by-step explanation:
it's closer to 13000 than to 12000
Answer:
13000Step-by-step explanation:
12628 >>>13000
Me:
This is easy like what grade are you in?
What is the y-intercept for this function?
y = x2 - 2x - 3
Answer:
-3
Step-by-step explanation:
Find the surface area of the rectangular prism (above) using its net (below).
Correct answer will receive a cookie and branilist
Answer:
62
Step-by-step explanation:
15+15+10+10+6+6= 62
Need the answer for x and y
Answer:
See below
Step-by-step explanation:
There is no 'y' in your question but I will answer the Q in the pic:
the two sides are equal so
10x-1 = 8x+11
2x = 12
x = 6 then CD = 8x+11 = 8(6)+ 11 = 59 units
A minute- hand of a clock is 16 in long. Find the distance traveled by the tip of the minute - hand in one hour.
The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?
9514 1404 393
Answer:
12 ft
Step-by-step explanation:
Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...
A = LW
264 = (2w-2)w
132 = w² -w . . . . . . . divide by 2, eliminate parentheses
132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square
√132.25 = w -0.5 . . . . . take the square root
0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root
The width of the living room is 12 feet.
WILL MARK BRAINLYEST
A street sign is 8 feet tall and casts a shadow that is 28 feet long. At the same time, a nearby tree casts a shadow that is 210 feet long. How tall is the tree?
A.60
B.70
C.80
D.90
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
Find the dot product of vectors u = -4i + 7j and v = 2i + j
Answer:
The desired dot product is -1
Step-by-step explanation:
To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:
dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1
The desired dot product is -1
HELP PLEASEEEE!!! SOMEONE HELP ME FOR ONCE, NO ONE IS ANSWERING MY QUESTIONS AND IM SO FREAKING STRESSED OUT. OH MY GOD SOMEONE PLS IM BEGGING YOU EXPLAIN YOUR ANSWER STEP BY STEP FOR ONCE
In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
a) 112,000 members
b) 78,000 members
c) 151,000 members
d) 127,000 members
Answer:
I have come to the conclusion that it is A. 112,000
Answer:
d) 127,000 members
Step-by-step explanation:
In this problem we have an exponential function of the form
where a is the initial value
b is the base
The base is equal to b=1+r
r is the average rate
In this problem we have a=23,000 members
r=5%=5/100=0.05
b=1+0.05=1.05
substitute
x ----> is the number of years since 1985
How many members will there be in 2020?
x=2020-1985=35 years
substitute in the function
Round to the nearest thousand
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answer:
It is 47.5 or 47 1/2
Step-by-step explanation:
The formula for volume of a prism is base x height.
The base is the area of the rectangle at the bottom. The area of a rectangle is, of course, length times width, so 2.5 x 4=10.
So, the base is 10.
Now, the second part of the formula is height.
The height is 4.75.
Now, do the formula: Base x height : 10 x4.75
The answer is 47.5.
Don't report me lol. I promise it is correct.
Answer:
I need 5 Brainliest before I can become Ace
Step-by-step explanation:
17. An equation is shown.
3x7=+7
What number makes the number sentence true?
A 3
B, 14
C. 21
D. 28
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
Total
Have running shoes
0.23
Have basketball shoes
No basketball shoes
Total
No running shoes
0.31
0.32
0.14
What percentage of the people surveyed have basketball shoes?
A. 37%
B. 54%
O C. 46%
O D. 63%
PLEASE HELP!!!!!!!!!! BRAINLIEST
Add the following fractions. Simplify and reduce to the lowest terms.
9/16 + 3/16
Answer:
3/4
Step-by-step explanation:
12/16
divided by 4
3/4
Answer: /34
Step-by-step explanation:
9/16 + 3/16
=(9+3)/16 ⇔ Fractions with the same denominator can subtract or add
=12/16 ⇔ Simplify
=(3×4)/(4×4) ⇔ Factor each number
=3/4 ⇔ Divide 4 on both numerator and denominator
Hope this helps!! :)
Please let me know if you have any questions