Question

The cost of manufacturing calculators can be modeled by the following equation, where c(p) represents the cost, in thousands of dollars, and p represents the number of units.
c(p) = p^2 - 28p + 250
Rewrite this function in the form that reveals the minimum of the function.

Answer 1

Rubric: (1 point) The student correctly chooses the form that reveals the maximum or minimum of the quadratic function (e.g., A).

Answer 2

Answer: p = 14

Given that $c(p) = p^2 - 28p + 250$

For the function to be minimize, simply derivate the given function with p and equate to zero

$(\frac { d }{ dp } )c(p)\quad =\quad (\frac { d }{ dp } )({ p }^{ 2 }-28p+250)$

                   = 2p-28

       $(\frac { d }{ dp } )c(p)\quad =\quad 0$

                    2p-28 =0  

                    2p = 28

$p\quad =\quad \frac { 28 }{ 2 } \quad =\quad 14$

At the value of p = 14 the above function will get the minimum value .