The Auto Club of Japan sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Osaka Industries (Osaka) manufactures two types of roll bars for cars. Model RB1 is bolted to the car using existing holes in the car's frame. Model RB2 is a heavier roll bar that must be welded to the car's frame. Model RB1 requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model RB2 requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Osaka's steel supplier indicated that at most 40,000 pounds of the high alloy steel will be available next quarter. In addition, Osaka estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit for model RB1 and $280 per unit for model RB2.
The computer solution for the linear programming model is shown below.
Optimal Objective Value =
424000.00000
Variable
--------------------------
Value
--------------------------Reduced Cost
--------------------------
RB1
1000.00000
0.00000
RB2
800.00000
0.00000
Constraint
--------------------------
Slack/Surplus
--------------------------
Dual Value
--------------------------
1
0.00000
8.80000
2
0.00000
0.60000
3
4000.00000
0.00000
Variable
--------------------------
Objective Coefficient
--------------------------
Allowable Increase
--------------------------
Allowable Decrease
--------------------------
RB1
200.00000
24.00000
88.00000
RB2
280.00000
220.00000
30.00000
Constraint
--------------------------
RHS Value
--------------------------
Allowable Increase
--------------------------
Allowable Decrease
--------------------------
1
40000.00000
909.09091
10000.00000
2
120000.00000
40000.00000
5714.28571
3
96000.00000
Infinite
4000.00000
a. What are the optimal solution and the total profit contribution?
b. Another supplier offered to provide Osaka Industries with an additional 500 pounds of the steel alloy at $2 per pound. Should Osaka purchase the additional pounds of the steel alloy? Explain.
c. Osaka is considering using overtime to increase the available assembly time. What would you advise Osaka to do regarding this option? Explain.
d. Because of increased competition, Osaka is considering reducing the price of model RB1 such that the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain.
e. If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain.