Question

1.The Miami Beach City Council has offered to subsidize hotel development in Miami Beach, and it is hoping for at least two hotels with a total capacity of at least 1,400. Suppose that you are a developer interested in taking advantage of this offer by building a small group of hotels in Miami Beach. You are thinking of three prototypes: a convention-style hotel with 500 rooms costing $100 million, a vacation-style hotel with 200 rooms costing $20 million, and a small motel with 50 rooms costing $4 million. The City Council will approve your plans, provided you build at least one convention-style hotel and no more than two small motels.

(a) How many of each type of hotel should you build to satisfy the city council's wishes and stipulations while minimizing your total cost?

convention-style hotel(s)
vacation-style hotel(s)
small motel(s)

2.

Succulent Citrus produces orange juice and orange concentrate. This year the company anticipates a demand of at least 14,000 quarts of orange juice and 500 quarts of orange concentrate. Each quart of orange juice requires 10 oranges, and each quart of concentrate requires 50 oranges. The company also anticipates using at least 190,000 oranges for these products. Each quart of orange juice costs the company 50¢ to produce, and each quart of concentrate costs $2.00 to produce. How many quarts of each product should Succulent Citrus produce to meet the demand and minimize total costs?

orange juice	qt
orange concentrate	qt

3.

You are about to go live with a Latin music download service called iYayay that will compete head-to-head with Apple's iTunes^® (good luck!). You will be selling digital albums of regional (Mexican/Tejano) music for $5 each, pop/rock albums for $4 each, and tropical (salsa/merengue/cumbia/bachata) for $6 each. Your servers can handle up to 35,000 downloaded albums per day, and you anticipate on the basis of national sales, revenues from regional music will be at least five times those from tropical music. You also anticipate that you will sell at least 11,000 pop/rock albums per day as a result of the very attractive $4 price. On the basis of these assumptions, how many of each type of album should you sell for a maximum daily revenue?

regional music albumspop/rock music albumstropical music albums

What will your daily revenue be?

Answer 1