You and your best friend formed a partnership. You being the creative one, makes
costume jewelry. Your best friend, being business-minded, markets the jewelry that you
make. In a recent month, You and your best friend spent 1000.00 on raw materials to
make 50 pieces of jewelry for 25.00 each. Assuming that you were not required to pay
sales tax, your net profit depends on the number of pieces of jewelry they sell.
1. The problem includes three constants: the fixed cost of materials (P1000) the price
of each piece (P25) and the total number of pieces made (50).
a. What should be the largest value of n? The largest value of P?
b. What should be the smallest value of n? The smallest value of P?
c. Write an equation that shows algebraically how to compute the net profit given the
number of pieces of jewelry sold.
2. If there are 40 pieces of jewelry sold, how much should be the profit? Explain your answer.
It sounds like
(a) the cost per piece is 1000/50 = 20
(b) the selling price per piece is 25
so the profit is 5 per piece
see what you can do with that
To answer the questions, let's break down the information given:
1a. The largest value of "n" would be the total number of pieces of jewelry made, which is 50.
1b. The largest value of "P" would be the fixed cost of materials, which is P1000.
1c. To compute the net profit, we can use the equation:
Net Profit = Total Revenue - Total Cost
Total Revenue is the price of each piece multiplied by the number of pieces sold, which is 25 * n, where "n" represents the number of pieces sold.
Total Cost is the fixed cost of material, P1000.
So, the equation for net profit would be:
Net Profit = 25n - 1000
2. If there are 40 pieces of jewelry sold, to calculate the profit we can substitute the value of "n" into the equation:
Net Profit = 25 * 40 - 1000
= 1000 - 1000
= 0
The profit in this case would be zero since the total revenue generated from selling 40 pieces of jewelry is equal to the total cost of materials.