The Following Linear Programming Problem Has Been Written to Plan

question 63

Multiple Choice

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?

• A)750
• B)2500
• C)2750
• D)3250

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Definitions:

Working Backward

A problem-solving technique that identifies the final goal and the steps, in reverse order, that are necessary to reach the goal.

Sub-goals

Sub-goals are smaller tasks or objectives set as steps towards achieving a more significant goal, helping to organize and focus efforts.

Thinking

A cognitive process used to transform or manipulate information that may be either focused (i.e., solving problems with clear goals) or unfocused (i.e., invoking loosely related ideas without a clear purpose).

Information Given

The data or facts provided or available in a specific context or situation.