Business Applications of the Derivative - Calculus

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A candy store can sell 180 candy bars at 62
cents each. The store can sell 220 candy bars if
the price is 54 cents each. The total cost of
producing x candy bars is C(x)=3050-10x+0.04x2
cents.
a) What is the demand function?
b) How many candy bars should be
produced to maximize profit?
c)
What is the profit at this point?
d) What is the total cost for producing this
amount of candy bars?
e) What is the selling price of the candy
bar when the profit is maximized?
f)
How many candy bars should be sold at
the lowest cost for the candy store?
g) When the cost is minimized, what is the
store’s profit at this point?
The manager of an electronics store knows he
can sell 60 blank CDs when the price is $1.20
each. If the price is $1.50, only 48 CDs are sold.
The total cost function for x CDs is
C(x)=0.70x+15 dollars. Assuming linear
demand…
a) What is the demand function?
b) What is the price per CD when profit is
maximized?
c)
How many CDs should be produced and
sold to maximize profit?
d) How many CDs should be produced and
sold to minimize cost?
e) What is the store’s greatest possible
profit?
f)
What is the store’s revenue when it is
making the most profit?
g) What is the store’s cost when it is
making the most profit?
Suppose the demand for a product is $12 and
the total costs are C(x)=0.3x2+2x+5.
a) What is the revenue function?
b) What is the profit function?
c)
What is the maximum value of the
profit?
d) How many products are being sold to
obtain the maximum profit?
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