SOLUTION: Jack & Jill charge $23 for a custom painted water pail. They currently sell 110 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could se

Question 1063765: Jack & Jill charge $23 for a custom painted water pail. They currently sell 110 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sell 10 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 josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Look for a pattern in price, and how many pails sold.

PRICE SELL 23-1 110+10 23-2 110+2*10 23-3 110+3*10 . . 23-x 110+10x

x, amount subtracted from $23
y, amount of sales revenue

Sales revenue to expect,

Can you find the maximum value for y and at which x it occurs from this?

$17 per pail for best sales of $2890
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
See the lesson
    - Using quadratic functions to solve problems on maximizing revenue/profit
in this site, where I explained how to solve such problems.

See the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site to learn on how to find the maximum/minimum of a quadratic function.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Jack & Jill charge $23 for a custom painted water pail. They currently sell 110 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sell 10 more pails a month. What price will maximize Jack & Jill's income? If they charges this price, how much income should they expect?

The equation you need is: .
After FOILing the binomials, find the value of x (number of PRICE INCREASES), which is also the value that MAXIMIZES revenue, or R(x), by
using the formula for the x coordinate of the vertex ().
Substitute the value of x into the above equation or the FOILed form to get R(x), or maximum revenue.
Hint: You should get MAXIMUM REVENUE of:
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