Question

Formulate the LP Problem, but do NOT solve: A furniture manufacturer makes armchairs and benches. The company has a maximum of 200 labor hours available in the Cutting Department, a maximum of 480 labor hours available in the Finishing Department, and a maximum of 150 labor hours available in the Packaging Department. Each armchair requires two hours in the Cutting Department, four hours in the Finishing Department and one hour in the Packaging Department. Each bench requires one hour in the Cutting Department, three hours in the Finishing Department, and one hour in the Packaging Department. Suppose the company makes a profit of $181 from the sale of each armchair and $57 from the sale of each bench. Assuming that all items produced are sold, how many armchairs and how many benches should the company produce in order to maximize profit? Cut Finish Package 1. Define the variables (use x and y). [3 pt] 20 Armchair2 4 X=of tables made per day Bench 1 1 3 1 U-H of Chaits made per dar yzo 2. Write the objective and objective function (use P). (A word and an equation.) 12 pt) 3. Write the constraints. (Don't forget the non-negative constraints.) 17 pts]

Answer 1

Answer: питber of 1. Let x arm chairs and number of benches the company produce y 2. As the company makes a profit of $181 from the sale of each arm chair and 57 from the sale of each bench, and assuming that all items produced are sold, the profit function (objective function) is P 181x 57y - and the objective is to maximize P. wwwMA

3. The constraints are found by utilising the following information finishing packaging Department cutting 200 150 Maximum 480 labour hours available Each arm chair 2 hours 4 hours 1 hour requires Each bench 1 hour 3 hours 1 hour requires 2x+y<=200 4x+3y<=480 X+y<=150

Р 3 181х + 57у max subject to 2х + у < 200 4х + 3у < 480 х+у< 150 х 2 0, у 20

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