B 41 1 2 40 40 1. (25 Points) A tool shop has four presses it uses to produce metal covers. All four presses operate differently. The tool shop produces three products under a recent contract. The contract requires the tool shop to produce at least 450 items of product #1, 600 items of product #2 and 320 items of product #3. The time in minutes) it takes to produce each product on each of the presses is given in the following table. Minutes PRESS PRODUCT D 35 34 39 36 32 43 3 38 37 33 Press A is available for 150 hours, Press B is available for 240 hours, Press C is available for 200 hours and Press D is available for 250 hours. The net profit for each combination of product that is produced on each press is given in the following table. Profit/Item PRESS PRODUCT A C 1 $7.80 $7.80 $8.20 $7.90 $6.70 $8.90 $9.20 $6.30 3 $8.40 $8.10 $9.00 $5.80 The tool shop wants to determine how many items of each product to produce on the respective presses in order to make the largest profit. Formulate the linear programming problem that will yield the most profitable production plan. DO NOT ATTEMPT TO SOLVE! a. Completely define the decision variables: B D 2 b. Define and mathematically formulate the objective function: c. Mathematically formulate all relevant constraints (use the back of this sheet if needed)