A manufacturer of souvenir items makes key rings which sell for $5.80 each. The cost of manufacturing is $1250 to set up the process, and then $0.80 per key ring.
1) Write a rule for the income in dollars, S, from selling n of these key rings.
2) Write a rule for the profit in dollars, P, from selling n of these key rings.
3) Find the number of key rings that must be sold to break even.
See previous post: Thu, 12-22-16, 11:14 PM.
1) To write a rule for the income in dollars, S, from selling n key rings, we need to consider the selling price of each key ring and the total number of key rings sold.
The selling price per key ring is $5.80. Therefore, the income from selling n key rings can be calculated by multiplying the selling price by the number of key rings:
S = 5.80n
So, the rule for the income is S = 5.80n.
2) To write a rule for the profit in dollars, P, from selling n key rings, we need to consider the total cost of manufacturing and the income generated from selling the key rings.
The cost of manufacturing is a fixed cost of $1250 to set up the process, and then an additional $0.80 per key ring. Therefore, the total cost of manufacturing n key rings can be calculated as:
Cost of manufacturing = 1250 + (0.80n)
The profit is obtained by subtracting the cost of manufacturing from the income generated from selling the key rings:
P = S - (1250 + 0.80n)
Simplifying this equation, we get:
P = 5.80n - 1250 - 0.80n
P = 5.00n - 1250
So, the rule for the profit is P = 5.00n - 1250.
3) To find the number of key rings that must be sold to break even, we need to determine the point where the profit (P) equals zero.
Setting the profit equation P = 0, we have:
0 = 5.00n - 1250
Adding 1250 to both sides of the equation, we get:
1250 = 5.00n
Dividing both sides of the equation by 5.00, we have:
n = 1250 / 5.00
Calculating this, we find that the number of key rings that must be sold to break even is 250.
So, you need to sell 250 key rings to break even.