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 many units of resource one the first constraint) are used if the company produces 10 units of product 1 and 5 units of product 2?

Question

Quizplus · Accepted Answer

In the first constraint, the left-hand side represents the amount of resource one used in the production process, which must be less than or equal to the total available amount (200). If we substitute the given production quantities (10 units of product 1 and 5 units of product 2) into the constraint, we get:
3*10 + 7*5 = 45
Therefore, the company would use 45 units of resource one if they produce 10 units of product 1 and 5 units of product 2.
As for the best choice(s), we would need additional information about the company's goals and constraints, such as the availability of other resources or market demand for each product. Without such information, we cannot determine the best choice(s) based solely on the given linear programming problem.

The Following Linear Programming Problem Has Been Written to Plan