Company ABC manufactures and sells widgets. The cost, in dollars, to produce x w

Question

Company ABC manufactures and sells widgets.
The cost, in dollars, to produce x widgets is given by C(x) = 330.50 + 4.20x for x 0,
and the price-demand function, in dollars per widget, is p(x) = 18 - 0.02x for 0 x 900.

(a) Find and interpret C(50).

(b) Find and interpret C (50). (Note that C (x) is the average cost function.)

(c) Find and simplify the expression for the revenue function R(x). (work optional)

(d) Find and simplify the expression for the profit function P(x). (work optional) Note that p(x) and P(x) are different functions.

(e) Find and interpret P(50), where P(x) is the profit function in part (d).

Explanation / Answer

C(x) = 330.50 + 4.20 x

C(50) = 330.50 + 4.20(50)

C(50) = 540.50

b) C(50) is the cost when 50 widgets are produced

c) revenue = price * quantity

R(x) = (18 - .02 x)x

R(x) = 18x - .02x^2

d) Profit = revenue - cost

P(x) = 18x - .02x^2 -  330.50 - 4.20 x

P(x) = -.02x^2 + 13.8 x - 330.50

e) P(50) = -.02(50)^2 + 13.8 (50) - 330.50

= 309.5

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.