a. Based on this solution, what are the labor costs for Trojan Manufacturing, i.e., the optimal objective function value?

b. If Worker B was only paid as much as Worker A ($10 per hour), would Fred ask Worker B to work more hours? Explain. What is the objective function value if Worker B is paid this new rate?

c. Ignoring (b), if Worker A had to work a minimum of 4 hours what is the resulting objective function value, or would the LOP need to be resolved? Explain.

d. Ignoring (b) and (c), if the demand for widgets goes down to 18 per month what is the new objective function value, or would you need to resolve?

1. The demand for widgets is 60 per day. Each worker can product the widgets at the following rates: Worker A B Capacity (Widgets/hour) 5 6 5 Fred needs to determine how many hours each worker needs to work to minimize labor costs (workers can work fractions of hours) including staying under his budget of $150 per day and still meet customer demand. The formulation of the linear optimization problem is as follows: Decision Variables A = hours Worker A is asked to work per day B = hours Worker B is asked to work per day C = hours Worker C is asked to work per day Objective Function: Min 10A + 12B + OC Constraints A Max A 2 B Min B => 2 Budget 12A +10B = 60 Non-negativity A, B, C >=0 After solving a linear optimization problem, Fred comes up with the following Sensitivity Table: Variable Cells Cell Name $B$11 A Hours $B$12 B Hours $B$13 C Hours Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 2 0 10 1E+30 0 5 0 0 12 4 0 0 10 1E+30 12 Constraints 4 Cell Name $B$19 A max Hours $B$20 B max Hours $B$21 Cmax Hours $B$22 A min Hours $B$23 B min Hours $B$24 C min Hours $B$25 Budget $B$26 Demand Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 2 0 8 1E+30 6 5 0 8 1E+30 3 -10 4 3.6 3.6 2 0 2 3.6 2 5 2 3 1E+30 4 0 0 4 1E+30 80 0 150 1E+30 70 60 2 60 18 18 0