Linear Programming

Question

Set up and solve the following:
Manufacturing TV’s and VCR’s requires the use of the assembling and the finishing departments of the factory according to the following schedule.
                   Hours per VCR               Hours per TV          Hours Available
Assembly              2                                 3                            12
Finishing               2                                 1                             8
VCR’s have a profit of $40 and TV’s have a profit of $32. How many VCR’s and how many TV’s should be manufactured to make a maximum profit?

Answer 1

Let x = number of TVs and y = number of VCRs.  The profit is:

 

Profit = 32x + 40y

 

Now you need a system of inequalities to represent your constraints on assembly and finishing:

 

Assembly:  3x + 2y ≤ 12

Finishing:  1x + 2y ≤ 8

Both: x ≥ 0, y ≥ 0

 

Graph the 4 inequalities.  The feasible zone - the area of the xy plane that contains solutions - is the area bounded within these 4 inequalities.  The feasible zone will have several vertices  -places where the inequalities intersect - along its outside perimeter.  The maximum profit will be at one of these vertices.  Identify the coordinates of each vertex and plug the x and y values into the profit equation.  The vertex with (x,y) values that yields the highest profit is the answer.