A company sells sets of kitchen knives The Basic Set consist

A company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef\'s knife. The Regular Set consists of 2 utility knives, 1 chef\'s knife, and 1 slicer. The Deluxe Set consists of 3 utility knives, 1 chef\'s knife, and 1 slicer. The profit is $30 on the Basic Set, $40 on the Regular Set, and $60 on the Deluxe Set. The company has on hand 800 utility knives, 400 chef\'s knives, and 200 slicers.

a. How many sets of each type should be made up and sold in order to maximize the profit?

b. What is the maximum profit?

Approach:

- Clearly state the objective fuction and constraints of the linear programming problem.

- State the initial simplex tableau.

- State the final simplex tableau.

Solution

Utility Chef Slicer Profit x Basic 2 1 0 30 y Regular 2 1 1 40 z Deluxe 3 1 1 60 800 400 200 Objective is to maximise profit Profit 30x+40y+60z Constraints: 2x+2y+3z <=800 Solve for the equalities first x+y+z<=400 y+z<=200 2x+2y+3z =800 x+y+z=400 y+z=200 Solution is x =200, z=0 y = 200 Or II set of solutions x=0, y =0, z=200 Profit 14000 Profit 12000 Hence 200 basic, 200 regular and no deluxe should be sold to maximise profit. Maximum profit 14000