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
$\begin{array} { l l } \text { MAX: } & 150 X _ { 1 } + 250 X _ { 2 } \\\text { Subject to: } & 2 X _ { 1 } + 5 X _ { 2 } \leq 200 \\& 3 X _ { 1 } + 7 X _ { 2 } \leq 175 \\& X _ { 1 } , X _ { 2 } \geq 0\end{array}$ How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Question

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

\begin{array} { l l } \text { MAX: } & 150 X _ { 1 } + 250 X _ { 2 } \\\text { Subject to: } & 2 X _ { 1 } + 5 X _ { 2 } \leq 200 \\& 3 X _ { 1 } + 7 X _ { 2 } \leq 175 \\& X _ { 1 } , X _ { 2 } \geq 0\end{array}

How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Quizplus · Accepted Answer

The profit is calculated as 150(10) + 250(5) = 1500 + 1250 = 2750.

The Following Linear Programming Problem Has Been Written to Plan