a baker estimates that it costs C(q)=0.07q^2+6q+300 Dollars each day to bake loa

Question

a baker estimates that it costs C(q)=0.07q^2+6q+300 Dollars each day to bake loaves of bread. How many loaves should be baked daily in order to minimize the average cost? (Round you answer to the nearest Internet)
_____________loaves a baker estimates that it costs C(q)=0.07q^2+6q+300 Dollars each day to bake loaves of bread. How many loaves should be baked daily in order to minimize the average cost? (Round you answer to the nearest Internet)
_____________loaves a baker estimates that it costs C(q)=0.07q^2+6q+300 Dollars each day to bake loaves of bread. How many loaves should be baked daily in order to minimize the average cost? (Round you answer to the nearest Internet)
_____________loaves

Explanation / Answer

C(q)=0.07q2+6q+300

Average cost is C(q) /q

==> AC(q) = [0.07q2+6q+300]/q

==> AC(q) = 0.07q+6+300/q

(d/dq)(AC(q)) = 0.07 -300/q2

To minimize the cost equate (d/dq)(AC(q)) to 0

==> 0.07 -300/q2 = 0

==> 300/q2 = 0.07

==> q2 = 300/0.07

==> q2 = 4285.7

==> q = squareroot(4285.7)

==> q = 65.465

==> q = 65

Hence in order to minimize the cost 65 loaves of bread are to be baked

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