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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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      Log On


   

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) About Me  (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, y=%2823-x%29%28110-10x%29

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(52784) About Me  (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) About Me  (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: R%28x%29+=+%28110+%2B+10x%29%2823+-+x%29.

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 (x+=+-+b%2F%282a%29).

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: highlight_green%28%22%242%2C890%22%29