# Maximizing Profit and Minimizing Surface Area of a Cylinder

9) A shop can sell 30 radios at $20 each, per week. For every $1 increase in the price there will be a loss of one sale per week. How much should the shop charge in order to make the maximum profit If the cost to make each radio is $10

10). A closed can (top and bottom), in the shape of a cylinder, is to hold 2000pi cm^3 of soup. Find the dimensions of the can of the least surface area.

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#### Solution Preview

Problem #9

Suppose each radio is charged x dollars more, then the selling price is 20 + x dollars each. But it results in x sales lost per weeks. So each weak it can sell 30 - x radios. The cost for these radios is 10(30 - x) dollars. So ...

#### Solution Summary

Maximizing Profit and Minimizing Surface Area of a Cylinder using derivatives is investigated.

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