A retailer notes that for a certain brand of dishwashing liquid, when the price is $10, the quantity sold per month is 700 and when the price is $12, the quantity sold per month is 500. If the relationship between price and quantity sold is linear, find the price when the revenue at its maximum.
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let the price be increased by $x above $10, then
revenue R = (10+x)(700 - 100x) = -100x^2 -300x +7000
R' = -200x -300 & R" = -200, so setting R' to zero will give a maxima
-200x - 300 = 0
x = -1.5
ans: $8.50
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revenue R = (10+x)(700 - 100x) = -100x^2 -300x +7000
R' = -200x -300 & R" = -200, so setting R' to zero will give a maxima
-200x - 300 = 0
x = -1.5
ans: $8.50
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