SOLUTION: Joe's Home Store finds that at a price of p = $30 each they would sell x = 64 hand saws each month. However, if they lower the price to p = $15, then they can expect to sell x = 79

Question 442511: Joe's Home Store finds that at a price of p = $30 each they would sell x = 64 hand saws each month. However, if they lower the price to p = $15, then they can expect to sell x = 79 saws in a month. Find the equation of the line for the above information. Write your answer in the form p = mx + b.
Hint: Use the slope formula first.
Joe's Home Store is looking for an equation to calculate revenue, or the amount of money that comes in from sales because business costs are subtracted. For a single product, we can find the revenue by multiplying the quantity of the product sold by the demand equation.
Hint: Substitute the result you found in question 3 into the equation R= xp to find the revenue equation. Provide your answer in simplified form.
Joe's Home Store has fixed costs, such as rent, insurance and wages, and variable costs, which are the costs to purchase the product they are selling. Joe's Home Store has fixed costs of $200 for saws and the variable cost for each saw is $5 each.
Find the cost equation for the saws. Write your answer in the form
C = mx + b.
To calculate profit subtract the costs from the revenue. Find the profit equation by substituting your equations for R and C into P = R - C. Simplify the equation.
What is the profit made from selling 20 saws each month?
What is the profit made from selling 25 saws each month?
What is the profit made from selling no tiles each month? Interpret your answer.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Joe's Home Store finds that at a price of p = $30 each they would sell x = 64 hand saws each month. However, if they lower the price to p = $15, then they can expect to sell x = 79 saws in a month. Find the equation of the line for the above information. Write your answer in the form p = mx + b.
Hint: Use the slope formula first.
---
You have 2 points (64,30) and (79,15)
slope = (15-30)/(79-64) = -15/15 = -1
---
30 = -1(64)+b
b = 94
---
Equation:
p = -x+94
------------------------

Joe's Home Store is looking for an equation to calculate revenue, or the amount of money that comes in from sales because business costs are subtracted. For a single product, we can find the revenue by multiplying the quantity of the product sold by the demand equation.
Hint: Substitute the result you found in question 3 into the equation R= xp to find the revenue equation. Provide your answer in simplified form.
---
R = x(-x+94) = -x^2+94x
-----------------------------------
Joe's Home Store has fixed costs, such as rent, insurance and wages, and variable costs, which are the costs to purchase the product they are selling. Joe's Home Store has fixed costs of $200 for saws and the variable cost for each saw is $5 each.
Find the cost equation for the saws. Write your answer in the form
C = mx + b.
C(x) = 5x+200
---------------------------
To calculate profit subtract the costs from the revenue. Find the profit equation by substituting your equations for R and C into P = R - C. Simplify the equation.
P(x) = -x^2+94x -(5x+200) = -x^2+89x-200
--------------------------------------------------------
What is the profit made from selling 20 saws each month?::1180
What is the profit made from selling 25 saws each month?:::1400
What is the profit made from selling no tiles each month? -200
Interpret your answer.$200 loss each month if no production.
Cheers,
Stan H.

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