SOLUTION: A local seafood shop sells lobster tails for $18 per tail. They sell an average 160 tails per week. Their research has determined that for each $0.50 decrease per tail, they would

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Question 181921: A local seafood shop sells lobster tails for $18 per tail. They sell an average 160 tails per week. Their research has determined that for each $0.50 decrease per tail, they would sell an additional 8 lobster tails per week. What should they charge per lobster tail to maximize their revenue?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A local seafood shop sells lobster tails for $18 per tail. They sell an average 160 tails per week. Their research has determined that for each $0.50 decrease per tail, they would sell an additional 8 lobster tails per week. What should they charge per lobster tail to maximize their revenue?
:
Let x = no. of 8 ea tails above 160 sold
Also x = no. of $.50 decreases from a cost of $18 per tail
:
Rev = no. sold * price
R = (160+8x)*(18-.5x)
FOIL
R = 2880 - 80x + 144x - 4x^2
R = -4x^2 + 64x + 2880
:
Find the axis of symmetry: x - %28-b%29%2F%282a%29
In this equation a=-4; b=64
x = %28-64%29%2F%282%2A-4%29
x = 8 ea $.50 decreases to for max sales
:
18 - (8*.50) $14 per tail for max revenue