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 MAX: 150 X1 + 250 X2 Subject to: 2 X1 + 5 X2 ≤ 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?

Answer 1

so we have:

`Max: 150x_(1) +250x_(2) \\\\st.\\2x_(1) +5x_(2) \leq 200\\3x_(1) +7x_(2) \leq 175\\\\x_(1) , x_(2) \geq 0`

Applying
`x_(1) = 10` and
`x_(2) = 5`, we have:

`150(10) + 250(5) = 1500 + 1250 = 2750`

`st.\\2(10) + 5(5) = 20 + 25 = 45 \leq 200\\3(10) + 7(5) = 30 + 35 = 65 \leq 175`

Thus, the company earned 2750 in profits and uses 45 units of resource one (the first constraint) and 65 units of resource two (the second constraint) if the company produces 10 units of product 1 and 5 units of product 2.

Solution:

The company earned 2750 in profits