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?

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

The objective function is mathematically represented as

=>    

Now the first constraints to this functions is

=>  

Another constraints to this function is

=>    

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  

   The profit of each ITC class is  

   The time require for  CWP  class is  

    The profit for   CWP  class is  

   The total time available  is

   the maximum number of trainee that can be accommodated in a daily basis is  

   The class size limit for  ITC  is  

    The class size limit for CWP is  

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

=>    

Now the constraints to this functions are

=>  

Another constraints to this function is

=>    

Here x and  y are the number of classes

answer: what do you mean

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.