Question

Crombie supermarket sells its own private label of canned peas as well as other national brands. The store makes a profit of $0.28 per can for its private label peas and a profit of $0.19 for any of other brands. The store has 6 square feet of shelf space available for canned pas, and each can of peas takes up 9 square feet of that space. Analytics show that each week the store sells less than half as many cans of its private label brand as it does the other national brands. The store wants to know how many cans of its own brand of peas and how many cans of the other brands to stock each week on the allocated shelf space in order maximize profits. a) formulate the problem of algebraically a linear programming model for this program. b) Solve this problem using excel.

Answer 1

There is a discrepancy in the question, the amount of space occupied by each can should be 9 squares inches. Total space of 6 square feet and 9 square feet per can makes no sense, you cannot fit even one can in that case

Now total cans that can be accomodated are

Problem Formulation

Constraints

Objective Function

Excel Output

Initialization

Solution