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Mathematics
Mathematics
Problem
Demand for a product is modeled by
q
=
400
−
2
p
q=400-2p
q
=
400
−
2
p
, where
p
p
p
is the price in dollars. Production cost is
C
(
q
)
=
0.5
q
2
+
1000
C(q)=0.5q^{2}+1000
C
(
q
)
=
0.5
q
2
+
1000
. Determine the quantity
q
q
q
that maximizes profit and state the corresponding maximum profit to the nearest dollar.
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