Question 1196506: The Times Herald Magazine is planning a special-edition magazine. The publishing expenses include fixed costs of $1400 and printing costs of 40 cents per magazine. The magazines will sell for $1.05 each.
Find:
a.) the linear cost of the function
b.) the linear revenue cost of the function
c.) the number of magazines to be sold to make a profit
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
x = number of magazines made and sold
0.40x = cost of printing x magazines, at $0.40 per magazine, before the $1400 fixed cost
0.40x+1400 = add on the $1400 fixed cost
Answer: C(x) = 0.40x+1400
=============================================================
Part (b)
revenue = amount of money coming in
revenue = (number of magazines sold)*(price per magazine)
revenue = (x)*(1.05)
revenue = 1.05x
Answer: R(x) = 1.05x
=============================================================
Part (c)
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 1.05x - (0.40x+1400)
P(x) = 1.05x - 0.40x - 1400
P(x) = 0.65x - 1400
Let's find the break-even point.
This is when the profit is $0
It is when the company neither loses money nor gains it.
Replace P(x) with 0. Solve for x.
P(x) = 0.65x - 1400
0 = 0.65x - 1400
1400 = 0.65x
x = 1400/0.65
x = 2153.84615384616 approximately
x = 2154
Let's see what the profit is for x = 2153 and x = 2154
P(2153) = 0.65*2153 - 1400 = -0.55
P(2154) = 0.65*2154 - 1400 = 0.1
Selling x = 2153 units produces a negative profit
Selling x = 2154 units is when the profit finally becomes positive.
Any larger x value will have P(x) > 0 since P(x) is linear.
Answer: The company must sell 2154, or more, magazines to make a profit.
|
|
|
