Q12. due by 1100pm central time USA. Find profit function, relationships, max pr
ID: 2900008 • Letter: Q
Question
Q12. due by 1100pm central time USA. Find profit function, relationships, max profit/min profit. thank you.
A company manufactures microchips. Use the revenue function R x-x 72-4x and the cost function C x = 122 + 14x to answer parts A- E where x is in millions of chips and R x and C x are in millions of dollars. Both functions have domain 1 SX 20 (A) Form a profit function P, and graph R, C, and P in the same rectangular coordinate systenm Which graph below shows R(x), C(x), and P(x)? The blue, dashed curve represents R; the pink line represents C, and the green, solid curve represents P A. OB. c. 20 20 20 20 (B) Discuss the relationship between the intersection points of the graphs of R and C and the x intercepts of P The x-values of the intersection points of R and C are (C) Find the x intercepts of P to the nearest thousand chips. Find the break-even points to the nearest thousand chips The x-intercepts of P occur at x =1 million chips | the x-intercepts of P (Use a comma to separate answers as needed. Round to three decimal places as needed.) Since the break-even point is the point at which the profit equals zero, do the x-intercepts of the profit function indicate the break-even points? O YesExplanation / Answer
(A) Profit P(x) = R(x) - C(x) = x(72-4x) - (122 + 14x) = x(58 - 4x) - 122
Graph (C), gives the correct description.
(B) The intersection of R and C shows that the Revenue and cost is equal at this point. The intersection with x-axis (i.e. x-intercept) the itm (C, R or P) is zero at that point.
x - intercept of R at x = 0 and x =18.
x - intercept of P at x = 2.667 (Approx) and x =11.833 (Approx.).
x - intercept of C at x = -7.71
(C) x = 2.667 millions = 2.667 x 100 Thousands = 266.7 Thousands, and at
x = 1183.3 Thousands
Break even point occurs at = x(72-4x) = (122 + 14x) , i.e. at x = 2.667 and x = 11.833 millions of chips
YES, x-intercepts represent the break - even - points.
(D) (i) Option (D) is correct.
(II) Option (A) is correct.
(E) Revenue R(x) = x (72 - 4x), Therefore, R'(x) = 72 - 8x =0, i.e. x= 9 [Maximum as R"(x) < 0]
Revenue at x = 9 is = 9 x (72 - 4 x 9) = 9 ( 72 - 36) = $ 324 Millions
Profit P(x) = x (58 - 4x) - 122, Therefore P'(x) = 58 - 8x, i.e. at x = 7.25,
Profit at x = 7.25 is = 7.25 (58 - 4 x 7.25) = 7.25 (58 - 29) = $ 210.25 Millions
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