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 Line 1 Line 2
A 11 5
B 6 9
Total Hours 65 40
a. Formulate a linear programming model to determine the optimal product mix that will maximize profit. Show Sensitivity Range for the coefficient of # of units of product A in the objective function and sensitivity Range for the coefficient of # of units of product B in the objective function.
b. What is the sensitivity ranges for the objective function coefficients?
c. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours