The Hong family owns 410 acres of farmland along the Yangtze Valley on which they grow potatoes and rice. Each acre of potatoes costs $165 to plant, cultivate, and harvest; each acre of rice costs $220. The Hongs have a budget of $77,000 for next year. If they plant over 200 acres of rice, worms will most likely destroy the crop. The profit from each acre of potatoes is $220; the profit from each acre of rice is $590. The Hongs want to know how many acres of each crop to plant in order to maximize their profit.

i. Formulate a linear programming model for this problem.

ii. Solve the above linear programming model graphically.

How many acres of farmland will not be cultivated at the optimal solution? How cautious are the Hongs when planting rice; how close do they come to planting 200 acres?

What would the profit for potatoes have to be for the Hongs to plant only potatoes?

If the Hongs can obtain an additional 110 acres of land, will the number of acres of potatoes and rice they plan to grow change?

If the Hongs decide not to cultivate a 40-acre section as part of a crop recovery program, how will it affect their crop plans?

iii. Solve the above linear programming model using "Excel Solver".

The Hongs have an opportunity to lease some extra land from a neighbour at $115 per acre, per season. Should the Hongs lease the land at that price?

The Hongs are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $2,000, would the number of acres of potatoes and rice they plant change? What is the maximum amount of money they should borrow?