 Math for Social Sciences II. Answer to Practice Exam.

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

• • Answer: • 2. Find the feasibility region in the following. Label any ``corner'' points of the region. (16 pts) , , , . Corner points: (0.0), (0,2), (5,0) and 3. Minimize z=4x+12y subject to: (18 pts) , , , .

Evaluate z at the corner points: (4,0), (12,0) and (6,4) Minimum: z= 16

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

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

f'(3)=2

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

• Find the marginal cost C'(x)

• Find and interpret C'(500)

Approximately the cost of the 501st pizza.

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

Answer: C(501)-C(500) = 6,006

• How are the answers in b and c related?

Answer: b approximates c

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 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?

Maximize r = 4x +6.5y

x=# of kilograms of mix

y=# of kilograms of mix

Subject to      The company should make 400kg of the mix

• 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?

Maximize 30x+20y

x =# of batches of cake

y =# of batches of cookies

Subject to      The bakery should make 3 batches of cake and 6 batches of cookies.

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Tue Nov 07 21:45:49 MDT 1997