Question

A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows. Product Hours/Unit Line 1 Line 2 A 12 4 B 4 8 Total hours 60 40 a) Formulate a linear programming model to determine the optimal product mix that will maximize profit. b) Transform this model into standard form.

Answer 1

Answer:

Following are the solution to the given question:

Explanation:

The decision variable of the green is defined in the given graph:

unit production of $A = X_1$

unit production of $B = X_2$

The objective function of the yellow is defined in the given graph:

maximize profit:

$\to 9X_1 + 7X_2$

Using the excel: $C10 = SUM(C8:C9)$

Constraints:

1)

For Line 1: maximum 60 hours

$\to 12X_1 + 4X_2 \leq 60, \ \ in \ excel: D4 \leq 60$

2)

For Line 2: maximum 40 hours

$\to 4X_1 + 8X_2 \leq 40, in\ \ excel: F4 \leq 40$

3) $X_1,X_2 \geq 0$

by solve the value we get $X_1 = 4, X_2 = 3,$ maximum profit $= 57$  

For point b:

$maximize: 9X_1 + 7X-2\\\\subject\ \ to:\\\\12X_1 + 4X_2 \leq 60\\\\4X_1 + 8X_2 \leq 40\\\\X1,X2 \geq 0$