University:
Santa Ana College
Course:
MATH 150 | Calculus for Biological, Management and Social Sciences
Academic year:

2023
Views:

32

Pages:

2
Author:

Cristofer Curtis

Math 150 Business Applications (Section 1.2-1.6) 1) The Dogs-R-Us Company has calculated the cost to build doghouses to be $50 each, plus a one-time set-up cost of $2100. a) Find the cost function C(x) C(x) = 50x + 2100 b) Find the revenue function R(x) R(x) = 75x c) Find the Profit function P(x) P(x) = R(x) - C(x) = 75x - (50x + 2100) P(x) = 25x - 2100 d) How many doghouses must be sold for them to break-even? P(x) = 0 25x - 2100 = 0 x = 84 doghouses must be sold to break-even e) Evaluate and Interpret P(250) P(250) = 4150 The profit from selling 250 doghouses is $4150. f) Find and Interpret the average rate of change from x=100 to x=150. AR of C in Profit = (P(150) - P(100)) / (150 - 100) = (4150 - 4000) / 50 = 25 When you sell from 100 to 150 doghouses, the profit is increasing on average $25/doghouse. 2) Joe's TV produces HD TV's. They have determined their cost function to be: C(x)=-2x²+x+10 while their revenue function is R(x)=x²+9x-6. a) The profit function P(x) P(x) = R(x) - C(x) = x² + 9x - 6 - (-2x² + x + 10) P(x) = 3x² + 8x - 16 b) P(2) and P(10) and interpret P(2) = 12 P(10) = 364 c) P'(x) P'(x) = 6x + 8 d) P'(2) and P'(10) and interpret P'(2) = 20 P'(10) = 68 3) An appliance manufacturer has determined that the cost, in dollars, of producing x espresso makers is C(x) = 3800 + 1.6x^0.5. If the revenue from the sale of x espresso makers is given by R(x) = 52x^0.9, find the rate at which the average profit per espresso maker is changing when 70 espresso makers are made and sold. Round to the nearest cent. (Interpret your answer) P(x) = R(x) - C(x) = 52x^0.9 - (3800 + 1.6x^0.5) P(x) = 52x^0.9 - 1.6x^0.5 - 3800 AP(x) = P(x)/x = (52x^0.9 - 1.6x^0.5 - 3800) / x AP'(x) = (46.8x^0.4 - 0.8x^-0.5 - 52x^-0.1 + 1.6x^-0.5 + 3800) / x^2 AP'(70) = 0.73 When 70 espresso makers are sold, the average profit is increasing $0.73/maker. 4) Algebraically, Find the equation for the tangent line to f(x) = (-2x^2 + 6) / (-3x - 2) at point (0, -3) f'(x) = (-4x + 2) / (-3x - 2)^2 f'(0) = 18/4 = 9/2 = m y - y₁ = m(x - x₁) y - (-3) = (9/2)(x - 0) y = (9/2)x - 3

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