# Math for Social Sciences II. Practice Exam.

1. Find the limit of the following functions: (12 points)

2. Find the feasibility region in the following. Label any ``corner'' points of the region. (16 pts)

, , , .

3. Minimize z=4x+12y subject to: (18 pts)

, , , .

4. Find the derivative of each of the following: (20 pts)

5. Use the definition of the derivative to find f'(3) if f(x)=2x+4 (7pts)

6. The cost of producing x pizzas is (7 pts)

• Find the marginal cost C'(x)

• Find and interpret C'(500)

• Find the exact cost to produce the 501st pizza.

• How are the answers in b and c related?

7. Set up the following problems. Indicate what the variables represent, the objective function and any constraints. (10 each)

• A candy company has 300 kilograms of chocolate-covered nuts and 100 kilograms of chocolate covered raisins to be sold as two different mixes. One mix will contain 1/2 nuts and 1/2 raisins and will sell for \$4 per kilogram. The other mix will contain 3/4 nuts and 1/4 raisins and will sell for \$6.50 per kilogram. How many kilograms of each mix should the company prepare for maximum revenue?

• A bakery makes both cakes and cookies. Each batch of cakes requires 2 hours in the oven and 3 hours in the decorating room. Each batch of cookies needs 1 and a half hours in the oven and 2/3 of an hour in the decorating room. The oven is available no more than 15 hours a day while the decorating room can be used no more than 13 hours a day. How many batches of cakes and cookies should the bakery make in order to maximize profits if cookies produce a profit of \$20 per batch and cakes produce a profit of \$30 per batch?