Question

The maximum production of a chips packing company is 5000 packages per day. The company produces teo types of chips, regular and diet. It costs $1.00 to produce each package of regular and $1.20 to produce each package of diet. The daily operating budget is $5400. The profit is $0.15 per regular and $0.17 per diet chips. How much of each type of chip is produced to obtain the maximum profit?

Answer 1

x= regular chips

y=diet chips

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The profit is $0.15 per regular and $0.17 per diet chips

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The maximum production of a chips packing company is 5000 packages per day

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It costs $1.00 to produce each package of regular and $1.20 to produce each package of diet. The daily operating budget is $5400.

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.

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the system is

subject to

graph both constraint

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The value of the objective function at each of these extreme points is as follows:

Extreme Point Coordinates (x,y)	Objective function value z=0.15x+0.17y
A(5000,0)	0.15(5000)+0.17(0)=750
B(3000,2000)	0.15(3000)+0.17(2000)=790
C(0,4500)	0.15(0)+0.17(4500)=765

The maximum value of the objective function z=790 occurs at the extreme point (3000,2000).

Hence, the optimal solution to the given LP problem is   

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3000 regular chips

2000 diet chips

maximum profit $790