Question

Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 2 lb of cast iron and 8 min of labor. To produce each model B grate requires 5 lb of cast iron and 5 min of labor. The profit for each model A grate is $2.50, and the profit for each model B grate is $2.00. 1300 lb of cast iron and 1200 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars? Maximize P = subject to the constraints cast iron labor model A y ≥ 0

Answer 1

Solution

With x units of model A and y units of model B,

‘The profit for each model A grate is $2.50, and the profit for each model B grate is $2.00.’ =>

Total profit, Z = 2.5x + 2.0y ………………………………………………………………………….. (1)

To produce each Model A requires 2 lb of cast iron and to produce each model B grate requires 5 lb of cast iron and 1300 lb of cast iron are available for the production of grates per day =>

2x + 5y ≤ 1300 …………………………………………………………………………………………. (2)

To produce each Model A requires 8 min of labor, to produce each Model B requires 5 min of labor and 1200 min of labor are available for the production of grates per day. =>

8x + 5y ≤ 1200 …………………………………………………………………………………………. (3)

(1) forms the objective function, (2) represents the cast iron constraint and (3) represents the labor constraint.

Thus, the LP formulation is:

Maximize Z = 2.5x + 2.0y

Subject to

2x + 5y ≤ 1300

8x + 5y ≤ 1200

x, y ≥ 0.

DONE