How many of each product should be made in order to maximize income?

Question

A company makes beef patties and beef empanadas. The oven can make 200 products per day. Each patty requires 2 oz. of filling and each empanada requires 1 oz. of filling. There are 250 oz of filling available. The income from each patty is $0.11 and from each empanada $0.05. How many of each product should be made to maximize income.

 

objective function

 

constraints

 

graph

 

vertices

 

optimization

Answer 1

The oven is used to make patties and empanadas, and can make 200 of them, maximum total, per day. Let p = number of patties and e = number of empanadas.

 

p + e ≤ 200

 

The total amount of filling available is 250, which is the maximum amount of filling that can be used.

 

2p + e ≤ 250

 

The above two inequalities are the constraints. We are seeking to maximize income, so the income equation is our optimization function. Let z = income.

 

0.11p + 0.05e = z

 

First, you want to draw out the constraint inequalities, with the lines and the shading. Then determine where the lines intersect ("corner point"). Plug the p and e values of that point into the income equation to determine z.