The following linear programming problem has been written to plan the production of two products.The company wants to maximize its profits.
X₁= number of product 1 produced in each batch X₂= number of product 2 produced in each batch
MAX: ^{150 X}₁^{+ 250 X}₂
Subject to: ^{2 X}₁^{+ 5 X}₂^{≤ 200}
3 X₁+ 7 X₂≤ 175 X₁,X₂≥ 0
How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Question

Quizplus · Accepted Answer

To find the profit earned with producing 10 units of product 1 and 5 units of product 2, substitute these values in the objective function and solve:

MAX: S1U1P1150(10) + 250(5) = 11,500
Subject to:
S1U1P12(10) + 5(5) ≤ 200S1S1P0
30 + 25 ≤ 200S1S1P0
55 ≤ 200S1S1P0
XS1U1B11 S1U1B0 ≤ 175 (from the second constraint)
Since the objective function is to maximize profit, the best choice is to produce 10 units of product 1 and 5 units of product 2, which results in a profit of 11,500.

The Following Linear Programming Problem Has Been Written to Plan