Suppose the Sunglasses Hut Company has a profit function given by Pa)0.0242 4 46
ID: 2888830 • Letter: S
Question
Suppose the Sunglasses Hut Company has a profit function given by Pa)0.0242 4 46, where q is the number of thousands of pairs of sunglasses sold and produced, and P(g) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Preview B) How many pairs of sumglasses (in thousands) should be sold to maximize profits? Ifnecessary, round your answer to three decimal places.) thousand pairs of sunglasses need to be sold. ) What are the actual maximum profits (in thousands) that can be expected? (Ifnecessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected.Explanation / Answer
multiple questions posted.please post each question seperately
1)
profit,P(q)= -0.02q2+4q-46
A)
marginal profit,MP(q)=P'(q)
=>MP(q) = -0.02*2q2-1+4*1-0
=>MP(q) = -0.04q+4
B)
for maximum profit ,MP(q)=0
-0.04q+4=0
=> 0.04q=4
=>q=100
100 thousand pairs of sunglasses need to be sold
C)
actual maximum profit =P(100)
actual maximum profit =-0.02*1002+4*100 -46
actual maximum profit =154
154 thousand dollars of maximum profits can be expected
B,C canbe solved with out differentiation.
P(q)= -0.02q2+4q-46
=>P(q)= -0.02(q2-200q) -46
=>P(q)= -0.02(q2-200q+(200/2)2-(200/2)2) -46
=>P(q)= -0.02(q2-200q+1002-1002) -46
=>P(q)= -0.02(q2-200q+1002)+(0.02*1002) -46
=>P(q)= -0.02(q-100)2 +154
parabolic curve is open downwards with vertex(maximum) at (100,154)
100 thousand pairs of sunglasses need to be sold
154 thousand dollars of maximum profits can be expected
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