VAMAP Assessment C 9h l https /www.wamap.org/assessment/showtest.php?action skip

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VAMAP Assessment C 9h l https /www.wamap.org/assessment/showtest.php?action skip&to-2; Course Messages Forums Gradebook Log Out Home Math&148 Business Calculus Assessment Jeongin Park Homework 8: 2.5 Due T 02/21/2017 4:59 pm ue Show Intro/Instructions Suppose the S Hut Coupany las a profit functiou giver by P(y) 0.03g 3g 24. when is the murzub of thousands of paens of sunglasses sold and produced and P(y) is the tot profit. thousands of Questions dollars, from selling and prodhucing g pairs of auglasses. Q 0/10) A) d a simplified expression for the marginal profit function. e sure to use the proper variable in your answer. Q 2 (0/10) Q3 (0/10) MP(g) Preview Q 4 (0/10) Q 5 (0/10) B) How many pairs ofsunglasses (in thousands) should be sold to maximize profits? If ary, round your answer to tuee decimal place Grade: 0/50 thousand pairs of sunglasses need to be sold. Print Versio What are the actual maximum profits (in thousands) duat can be expected? If necessary. Iouud you: answer to ulmee decimal place Answer: thousand dollars of maximum profits can be expected. Get help: Vadeo Points possible: 10 This is attempt 1 of 5. Post this question to forum Submit 5.3 t 2017-02-20

Explanation / Answer

The quadratic function, P(q) = -0.03q2 + 3q - 24, has a negative value for a, meaning the parabola will be inverted . This represents the x-coordinate of the vertex and the answer to Part A.

(A) marginal progit function P'(q) = -0.06q + 3 = 0

q = 50

So q=50 will be the maximum profit point. You can find the actual profits by plugging in to the original equation.

B. 50,000 pairs of sunglasses should be sold to maximize profits.

To find the actual maximum profits, we plug in 50 to the function and solve to find the y-coordinate of the vertex.

P(q) = -0.03(50)2 + 3(50) - 24

P(q) = -0.03(2500) + 150 - 24

P(q) = -75 +150 - 24

P(q) = 41

so

(B) The actual maximum profits are $41,000.

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