Gabrielle D.
asked • 07/26/20The manufacturer of a brand of mattresses will make x hundred units available in the market when the unit price is
p = 200 + 70e0.04x
dollars.
(a) Find the number of mattresses the manufacturer will make available in the market place if the unit price is set at $350/mattress. (Round your answer to the nearest integer.)
( I found A, its 19.05)
(b) Use the result of part (a) to find the producers' surplus if the unit price is set at $350/mattress. (Round your answer to the nearest dollar.)
( I have a step by step video on how to do it but when I'm trying to solve for part B I get lost, can you explain how I can get B?)
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1 Expert Answer
Yefim S. answered • 07/27/20
Tutor
5
(20)
Math Tutor with Experience
(a) You get right, x = 19 (rounded to intergers)
(b) Producer's surplas PS = ∫019(350 - 200 - 70e0.04x)dx = (150x - 70/0.04e0.04x)019 = (150x - 1750e0.04x)019 =
= 150·19 - 1750e0.76 + 1750 = $858
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Sidney P.
a) Since x is hundreds of items, actual number of mattresses = 1905. b) I assume "surplus" is profit, but we can't determine that without knowing the cost per item (or per 1 hundred units in this case).07/26/20