Mathematics

Mathematics

Problem

A manufacturer’s cost (in dollars) to produce pp units is modeled by C(p)={0.5p2+60,0≤p≤20,20p+100,20<p≤40.C(p)=\begin{cases}0.5p^{2}+60,&0\le p\le 20,\\20p+100,&20<p\le 40.\end{cases} Identify the production level pp (to the nearest whole unit) that minimizes the cost on the interval 0≤p≤400\le p\le 40.

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