How do you get the equation for this problem
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How do you get the equation for this problem

[From: ] [author: ] [Date: 12-10-31] [Hit: ]
50 cents. What selling price should be set to maximize profit?I only figured ou part of the equation, and would appreciate it if you could help me understand how to add the expense cost to it.(40-4x) (8 + .Thanks,......
Hey I have a math test tomorrow and this one review question confused me:

A girl makes and sells shell necklaces. The material for each necklace costs her $4. She has been selling them for $8 each and averaging sales of 40 a week. She found she would lose 4 sales a week by increasing her price by .50 cents. What selling price should be set to maximize profit?

I only figured ou part of the equation, and would appreciate it if you could help me understand how to add the expense cost to it.

(40-4x) (8 + .50x)

Thanks, 10 points best answer

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Let x = the # of necklaces she sells.
Let y = her profit (in $)

Let's start with the first equation.
The material starts with $4 costs per necklace.
Therefore, it is y = -4x.
She sells each for $8 per necklace, so you add 8x.
y = -4x + 8x = 4x
Therefore, y = 4x.
She sells 40 necklaces per week, so x = 40 for the first equation.
y = 4 (40) = $160

Next, the second equation.
She increases the price by $0.50, so you add 0.50x.
y = 4x + 0.50x = 4.5x
Therefore, y = 4.5x.
She loses 4 sales per week by increasing the price, so x turns from 40 to 36.
y = 4.5 (36) = $162

$162 is more than $160, so she should increase the price by $0.50 to maximize profits.
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