Question

James owns a cafe. A mathematical model connecting profit from selling coffee (in dollars) and x, the price per cup of coffee (in dimes) is `p(x)= -x^2+ 35x+ 34`, how do you find the profit per day if the price per cup of coffee is $1.80?

Answer 1

`$340`

Explanation:

If a cup of coffee costs `$1.80` then it costs `18` dimes.

The profit function `p(x)=-x^2+35x+34`
gives the the profit `p` in dollars given a price per cup `x` in dimes.

Substituting `18` (dimes) for `x` gives
`color(white)("XXX")p(18)=-(18^2)+(35xx18)+34`
`color(white)("XXXXXX")=-324+360+34`
`color(white)("XXXXXX")=340` (dollars)