Solved (Free): A company produces two products that are produced on 2 assembly lines. Assembly line 1 has 100 available hours and assembly line 2 has 42 available hours

ByDr. Raju Chaudhari

Apr 6, 2021

A company produces two products that are produced on 2 assembly lines. Assembly line 1 has 100 available hours and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line one, while on line 2, product 1 requires 7 hours and product 2 requires 3 hours. The profit of product 1 is \$6 per unit, and the profit for product 2 is \$4 per unit.

Formulate a linear programming model for this problem.

Solution

Let the company produces $x_1$ and $x_2$ units of First type product and second type of product respectively.

Given information can be summarized in the table form as :

Assembly \ Product First Type Product Second Type Product Availability
Assembly Line 1 10 hours 10 hours 100 hours
Assembly Line 2 7 hours 3 hours 42 hours
Profit per unit \$6$4

Profit per unit for first type product is \$6, so for$x_1$units of first type product the profit will be \$ $6x_1$.

Profit per unit for second type product is \$4, so for$x_2$units of second type product will be \$4 $x_2$.