Question

This is the slack time of year at JES, Inc. The firm would actually like to shut down the plant, but if it laid off its core employees, they would probably go to work for a competitor. JES could keep its core (full-time, year-round) employees busy by making 10,000 round tables per month, or by making 20,000 square tables per month (or some ratio thereof). JES does, however, have a contract with a supplier to buy minimum of 5,000 square tabletops per month. Handling and storage costs per round table will be $10; these costs would be $8 per square table. Let Xi = thousands of round tables per month, X2 = thousands of square tables per month. Create a set of linear equations to describe the objective function and the constraints (enter your responses as whole numbers) Objective function: Minimize Z (in thousands) = 10 X, + 8 X 5. Constraints Square tabletop requirement 0 X, + 1X2 2 Total labor capacity: 2X, + 1X2 2 20 Nonnegativity: X, X220.

what is the optimal solution? how many thousand round tables and how many thousand square tables?

Answer 1

Looks like you have already done the first part and looking to obtain only the solution. Then, assuming that the LP formulation is correct, we can solve it to obtain the solution.

Minimize 10X1 + 8X2

Subject to

0X1 + 1X2 >= 5

2X1 + 1X2 >= 20

X1, X2 >= 0

The solution for this LP is shown below

LINDO X File Edit Solve Reports Window Help <untitled> - @ X LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1) 115.0000 Rel Minimize 10X1 + 8X2 Subject to OX1 + 1X2 >= 5 2X1 + 1X2 >= 20 VARIABLE X1 VALUE 7.500000 5.000000 REDUCED COST 0.000000 0.000000 X2 ROW 2 ) SLACK OR SURPLUS 0.000000 0.000000 DUAL PRICES -3.000000 -5.000000 NO. ITERATIONS- RANGES IN WHICH THE BASIS IS UNCHANGED: VARIABLE OBJ COEFFICIENT RANGES ALLOWABLE ALLOWABLE INCREASE DECREASE 6.000000 10.000000 INFINITY 3.000000 CURRENT COEF 10.000000 8.000000 X1 X2 ROW CURRENT RHS 5.000000 20.000000 RIGHTHAND SIDE RANGES ALLOWABLE INCREASE 15.000000 INFINITY ALLOWABLE DECREASE 5.000000 15.000000

The optimal solution is to produce 7.5 thousand round tables and 5 thousand square tables. The cost will be 115 thousand