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Derivatives : Maximum and Minimum Values

5). The total cost of producing x radio sets per day is $ ( 1/4 x^2 + 35x + 25 ) and the price per set is at which they may be sold is $ ( 50 - 1/2x ). Find the daily output for maximum profit.

Answer 10 sets /day

6). The cost of fuel in running a locomotive is proportional to the square of the speed and is $25/hr for a speed of 25km/hr. The other costs are $100 /hr regardless of speed. Find the speed that will make the cost per kilometer a minimum.

Answer 50km/hr

8) A rectangular field , to enclose a given area , is fenced off along a straight river. If no fencing is needed along the river , show that the least amount of fencing will be required when the length of the field is twice the width ( this is all the info available- the condition ? length =2x width).

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5). The total cost of producing x radio sets per day is $ ( 1/4 x^2 + 35x + 25 ) and the price per set is at which they may be sold is $ ( 50 - 1/2x ). Find the daily output for maximum profit

Answer 10 sets /day
The cost is
The revenue is
Therefore, the profit function is

The critical point is

, so according to the second derivative test, at the only critical point, the point is maximum.
The daily output is 10 so that the profit is maximized.

6). The cost of fuel in running a locomotive is ...

Solution Summary

Maximum and Minimum Values are found using derivatives.

$2.19