Math for Social Sciences II. Practice Exam.
- Find the limit of the following functions: (12 points)
- Find the feasibility region in the following. Label any
``corner'' points of the region. (16 pts)
,
,
,
.
- Minimize z=4x+12y subject to: (18 pts)
,
,
,
.
- Find the derivative of each of the following: (20 pts)
- Use the definition of the derivative to find f'(3) if f(x)=2x+4
(7pts)
- 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?
- 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?
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Tue Nov 07 21:45:49 MDT 1997
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