SOLUTION: Jack & Jill charge $20 for a custom painted water pail. They currently sell 80 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sel

Question 1060581: Jack & Jill charge $20 for a custom painted water pail. They currently sell 80 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sell 15 more pails a month. What price will maximize Jack & Jill's income? If they charges this price, how much income should they expect?
Found 3 solutions by josmiceli, josgarithmetic, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the number of $1 decreases in price
Let = the total income from sales of water pails
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[ income ] = [ price per pail ] x [ number of pails sold ]

The n-value of the vertex ( max in this case ) is:

-----------------------------
Going back to original equation:
[ price/pail ] =
The price that maximizes income is:

$12.33
-----------------------------
The max income at this price is:

$2,406.67
-----------------------
here's the plot:

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
r, income
x, how many pails sold
p, price per pail

n, each dollar decrease in price

PRICE x 20 80 20-1 80+15 20-2 80+2*15 20-3 80+3*15 20-n 80+n*15 or 80+15n

r is a parabolic function with zeros at , and the MAXIMUM revenue will be exactly in the middle of the two zeros for n.

--

-

-
MIDDLE n VALUE

----------how many dollars LESS THAN 20, for maximum revenue.

If Jack and Jill want a price to the nearest penny, then this would be $7.33 per pail.
Revenue would be .
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Jack & Jill charge $20 for a custom painted water pail. They currently sell 80 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sell 15 more pails a month. What price will maximize Jack & Jill's income? If they charges this price, how much income should they expect?

for a reduction of $7.33, or a reduced price of will maximize their income.
At a reduced price of $12.67, MAXIMUM income is:
Let no-one tell you otherwise!!
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