# A ﬁrm’s revenue after selling q items is given by R(q) = 2q3 +36q while the ﬁrm’s costs after making q items is C(q) = 3q^2 −10. (a) If the ﬁrm can make a maximum of 4 units, how many units should the ﬁrm make to maximize proﬁt. What is the proﬁt at this point? (b) If the ﬁrm can make a maximum of 10 units, how many units should the ﬁrm make to maximize proﬁt?

Question

A ﬁrm’s revenue after selling q items is given by R(q) = 2q3 +36q while the ﬁrm’s costs after making q items is C(q) = 3q^2 −10.

(a) If the ﬁrm can make a maximum of 4 units, how many units should the ﬁrm make to maximize proﬁt. What is the proﬁt at this point?

(b) If the ﬁrm can make a maximum of 10 units, how many units should the ﬁrm make to maximize proﬁt?

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MathCalculus

### Derivative 