The cost, in dollars, for a ompany to produce x widgets is given by c(x)=4500+5x

ID: 3033360 • Letter: T

Question

The cost, in dollars, for a ompany to produce x widgets is given by

c(x)=4500+5x for x greater than or equal to 0, and the price demand function, in dollars per widget, is

p(x)=50-0.05x for 0less than or equal to X less than or equal to 1000.

the profit function for the above scenario is p(x)+-0.05x^2+45x-4500.

a.) The profit function is a quadratic function and so its graph is parabola. does the parabola open up or down.

b.) find the vertex of the profit function P(x) using algebra. Show all work

c.) state the maximum profit and the number of widgets which yield maximum profit.

The maximum profit is___________when___________widgets are sold.

D.) determine the price to charge per widget in order to maximize profit.

e.) Find and interpret the break-even points. show all work.

a) p(x) = -0.05x^2 +45x - 4500

in quadratic equation ax^2 + bx +c =0 ; if a<0 parabola opens downwards

So, p(x) downwards

b) maximu profit would be at vertex:

x = -b/2a = -(45/2*-0.05) = 450 widgets

c) max profit : p(450) = -0.05(450)^2 +45(450) - 4500

= $ 5625

d) Beark even point where Cost = Reveneue

I.e. Profit =0 ; P(x) =0

-0.05x^2 +45x - 4500 =0

solve for x : x= 114.59 , 785.41 widgets

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