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)
 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 chocolatecovered 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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