Question 83171: #24
Marginal Cost of Coffee The manager of a restaurant
found that the cost to produce 100 cups of coffee is
$11.02, while the cost to produce 400 cups is $40.12.
Assume the cost is a linear function of x, the number
of cups produced.
a. Find a formula for C(x).
b. What is the fixed cost?
c. Find the total cost of producing 1000 cups.
d. Find the total cost of producing 1001 cups.
e. Find the marginal cost of the 1001st cup.
f. What is the marginal cost of any cup and what does this
mean to the manager?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The manager of a restaurant found that the cost to produce
100 cups of coffee is $11.02,
while the cost to produce 400 cups is $40.12.
Assume the cost is a linear function of x, the number of cups produced.
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You have two points: (100,11.02) and (400,40.12)
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a. Find a formula for C(x).
slope - [40.12-11.02]/[400-300] = 29.10/300 = 0.097..
Form is y=mx+b where y=31.02 when x=100 and m=0.097...
31.02 = 0.097(100)+b
31.02 = 9.7 + b
b= 21.32
EQUATION:
Cost(x) = 0.097x + 21.32
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b. What is the fixed cost? $21.32
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c. Find the total cost of producing 1000 cups.
C(1000) = 0.097(1000)+21.32 = $118.32
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d. Find the total cost of producing 1001 cups.
Add 9.7 cents the the cost of part c.
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e. Find the marginal cost of the 1001st cup.
The slope is the marginal cost: 9.7 cents
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f. What is the marginal cost of any cup and what does this
mean to the manager?
The marginal cost for any cup is 9.7 cents.
If he produces no cups his overhead is $21.32
For each cup he sells he gains 9.7 cents.
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Cheers,
Stan H.
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