After some consultants point out that the Acme Toy Company has two bottlenecks in its production of xylophones and yo-yos. The first is a critical grinding machine that only has 9 hours of capacity per day. The second is warehouse space which is limited to 10 (thousand) square feet. Each production run of xylophones requires 3 hours of grinding and take up two thousand square feet of storage while each yo-yo run requires one hour of grinding time and takes up 2000 square feet of storage. Each run of xylophones contributes $4 (thousand) to overhead and profit while each run of yo-yos contributes $2 (thousand).
- Find the optimal amounts of each kind of toy to produce using graphical methods.
- State and solve the dual problem graphically.
- Now solve the problem using the revised simplex method. Do you get the same answers?
- How much would the firm be willing to pay to increase the capacity of the grinding machine?