Problem of the Week

A new problem every Monday that challenges participants of all ages to think creatively and apply their math skills. Perfect for a weekly mental challenge.

Jean builds and sells skateboards. Jean has observed that the price for each skateboard (in $/unit) is given by the function: p(x) = -0.001x + 7.25 + 110937.5/x where x is the number of skateboards. 
Jean has also observed that the cost of building skateboards (in $) is given by the function:
C(x) = 4.75x + 50000. 

If Profit = Revenue – Cost, how many skateboards should Jean sell for Jean to maximize the profit?

(Note: Revenue = (x)(price per unit))

Problem submitted by Mike Schieffer, Austin, TX


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