Math for Social Sciences II. Answer to Practice Exam.

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

• Answer: -7

• Answer:

• Answer: diverges

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

, , , .

Answer:

Corner points: (0.0), (0,2), (5,0) and

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

, , , .

Answer:

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)

Answer:

f'(x)= 2

f'(3)=2

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

• Find the marginal cost C'(x)

Answer: C'(x)=12x

• Find and interpret C'(500)

Answer: C'(500)=6000

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?

Answer:

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?

Answer:

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.

If you would like to go back to the original menu, click on Menu.

Tue Nov 07 21:45:49 MDT 1997

Copyright © 1999-2019 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour