MAT 131 Sample Test 2

1. A woman wants to use milk and orange juice to increase the amount of calcium and vitamin A in her daily diet. An ounce of milk contains 37 mg (milligrams) of calcium and 57 mcg (micrograms) of vitamin A. An ounce of orange juice contains 5 mg of calcium and 65 mcg of vitamin A. How many ounces of milk and orange juice should the woman drink each day to provide exactly 500 mg of calcium and 1,200 mcg of vitamin A? Develop a mathematical model for this problem and use your model to answer the question. Illustrate the solution on a graph.

2. Federated Shipping, a national delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). A customer is billed \$29.95 for shipping a 5-pound package and \$59.20 for shipping a 20-pound package. What is the base price and the surcharge for each additional pound? Develop a mathematical model for this problem and use your model to answer the question. Illustrate the solution on a graph.

3. A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,000 cubic feet. Three different types of trucks are available: a 10-foot truck with a capacity of 350 cubic feet, a 14-foot truck with a capacity of 700 cubic feet, and a 24-foot truck with a capacity of 1,400 cubic feet. How many of each truck should the company purchase? Develop a mathematical model for this problem and use your model to answer the question.

4. An investment advisor has two types of investments available for clients. A conservative type of investment currently pays a return of 10% per year. A riskier investment currently pays a return of 20% per year. An client has \$50,000 to invest and wants a return of 15% per year. How much should the client invest in each type of investment? Develop a mathematical model for this problem and use your model to answer the question. Illustrate the solution on a graph.