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Math for Social Sciences II. Answer to Practice Exam.

Find the limit of the following functions: (12 points)
- Answer: -7
- Answer:
- Answer: diverges
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
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
Find the derivative of each of the following: (20 pts)
- Answer:
- Answer:
- Answer:
- Answer:
- Answer:
Use the definition of the derivative to find f'(3) if f(x)=2x+4 (7pts)
Answer:

f'(x)= 2
f'(3)=2
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
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.

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Tue Nov 07 21:45:49 MDT 1997