Assignment
1. A chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $400 and yields 300 units of A, 100 units of B, and 100 units of C. Running process 2 for an hour costs $100 and yields 100 units of A and 100 units of B. To meet customer demands, at least 1000 units of A, 500 units of B, and 300 units of C must be produced daily.
• Use Solver to determine a daily production plan that minimizes the cost of meeting the company's daily demands.
• Use a solver of your choice to see what happens to the decision variables and the total cost when the hourly processing cost for process 2 increases in increments of $0.50. How large must this cost increase be before the decision variables change? What happens when it continues to increase beyond this point? (hint: reduced cost may help to answer this question.)
2. A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $400 to profit, and a chair contributes $250. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 2000 units of wood available.
• Use Solver to maximize the company's profit.
• Confirm graphically that the solution in part a maximizes the company's profit.
• Do sensitivity analysis to see what happens to the decision variables and the total profit when the availability of wood varies from 1000 to 3000 in 100-unit increments.
Based on your findings, how much would the company be willing to pay for each extra unit of wood over its current 2000 units? How much profit would the company lose if it lost any of its current 2000 units?
(hint: dual/shadow price may help to answer this question)
3. A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted.
If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled.
It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company's profit.
(Hint: One approach, but not the only approach, is to try a graphical procedure first and then deduce the constraints from the graph.)