Hi-Tech, Inc., is a computer training company serving metropolitan Toronto, Canada. The firm contracts a group of part-time instructors to teach a variety of courses concurrently at its downtown location. While demand is so high that any class offered will be filled immediately, Hi-Tech is looking at only two courses at this time: Introduction to Computers (ITC) and Creation of Web Pages (CWP). Each ITC class requires 7.5 hours of preparation/instruction time and contributes a profit of $720, whereas each CWP class calls for only 3 hours and contributes $300. Available time for these two courses is limited to 56 hours a day. There is a restriction on the maximum number of trainees that can be efficiently handled. More specifically, at most 100 students can be accommodated on a daily basis without putting a strain on the facility and support staff. Additionally, each course has a class size limit - 6 for ITC and 12 for CWP. Hi-Tech would like to maximize the daily total profit from both courses so that it could offer certain other courses on a "goodwill" basis. Formulate an AILP for management to decide how many classes should be scheduled for each subject daily
What is the objective function?

Answer:

The  AILP for management to decide  how many classes should be scheduled for each subject daily is

The objective function is mathematically represented as

       [tex]M  =  P_c  *  a  + P_w  *  b[/tex]

=>    [tex]M  = 720  a  + 300  b[/tex]

Now the first constraints to this functions is

     [tex]t_c  *  x  + t_w * y  \le t_a[/tex]

=>  [tex] 7.5  x  + 3 y  \le 56[/tex]

Another constraints to this function is

     [tex]k  x  +  u  y  \le  N[/tex]

=>    [tex]6  x  +  2  y  \le  100[/tex]

Here x and  y are the number of classes    

Step-by-step explanation:

From the question we are told that

   The time required for each ITC class is  [tex]t_c  = 7.5 \ hours[/tex]

   The profit of each ITC class is  [tex]P_c  =  \$ 720[/tex]

   The time require for  CWP  class is  [tex]t_w  =  3 \  hours[/tex]

    The profit for   CWP  class is  [tex]P_w  =  \$ 300[/tex]

   The total time available  is [tex]t_a  =  56 \  hours / day[/tex]

   the maximum number of trainee that can be accommodated in a daily basis is   [tex]N  =  100[/tex]

   The class size limit for  ITC  is  [tex]k  =6[/tex]

    The class size limit for CWP is  [tex]u  =12[/tex]

Generally the aim of Hi-Tech is to maximize profit

So the objective function will be a function that maximizes profit

Generally the objective function is mathematically represented as

       [tex]M  =  P_c  *  a  + P_w  *  b[/tex]

=>    [tex]M  = 720  a  + 300  b[/tex]

Now the constraints to this functions are

     [tex]t_c  *  x  + t_w * y  \le t_a[/tex]

=>  [tex] 7.5  x  + 3 y  \le 56[/tex]

Another constraints to this function is

     [tex]k  x  +  u  y  \le  N[/tex]

=>    [tex]6  x  +  2  y  \le  100[/tex]

Here x and  y are the number of classes

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