Set up Exercises 27–31 for solution by the simplex method. First express the linear constraints and objective function, then add slack variables to convert each constraint into a linear equation, and then set up the initial simplex tableau. The solutions of some of these problems will be completed in the exercises for the next section.
Production—Knives The Cut-Right 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. Their profit is $30 on a Basic Set, $40 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef’s knives, and 200 slicers. Assuming that all sets will be sold, how many of each type should be produced in order to maximize profit? What is the maximum profit?
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Finite Mathematics (11th Edition)
- Just make the linear programming model of the next exercise: The maximum profit must be obtained in the manufacture of two products: pants and T-shirts. The first brings a profit of $325 and the second $185 per unit. Each product must go through two processes: manufacturing and finishing. The pants take 2 hours to manufacture and 1 hour to finish, while the shirts require 1.5 hours to manufacture and 3 hours to finish. Each department has 180 and 200 hours respectivelyarrow_forwardProduct Blend Example Petroleum Mix Inputs Component 1 2 3 Petroleum Mix Products Component Specifications Grade Super Premium Maximum Barrels Available/Day 4,500 2,700 3,500 Extra At least 50% of 1 Not more than 30% of 2 At least 40% of 1 Not more than 25% of 3 At least 60% of 1 At least 10% of 2 Cost/Barrel $12 10 14 Selling Price/Barrel $23 20 18 • Produce at least 3,000 Barrels of each grade.arrow_forwardWrite the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)arrow_forward
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