Problema Solution
The daily profit in dollars of a specialty cake shop is described by the function P(x) = -6x2 + 276x - 2688, where x is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?
Answer provided by our tutors
We can use Algebrator to graph the equation and see immediately that the vertex of the parabola is located at the point (23, 486), so that when 23 cakes are made the profit reaches $486.
We can also see that the vertex occurs at x=23 in the graphable form of the equation:
P(x) = -6(x-23)^2 + 486
since "-6(x-23)^2" is always a negative value and it is then maximized when x=23 since 23-23=0
The maximum profit is then reached when 23 cakes per day are prepared.