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).

1. Find the optimal amounts of each kind of toy to produce using graphical methods.
2. State and solve the dual problem graphically.
3. Now solve the problem using the revised simplex method. Do you get the same answers?
4. How much would the firm be willing to pay to increase the capacity of the grinding machine?