Question

Fantastic Flags, Inc. finds that the cost to make x flags is C=32x + 18,695, while the

revenue produced from them is R=36x (C and Rare in dollars). What is the smallest
whole number of flags, x, that must be sold for the company to show a profit?

Answer 1

at least 4674 flags should be sold to show a profit

Explanation:

The net profit is defined as the revenue (income from selling the flags) minus the cost (of producing the flags).

Since we want that profit (P) to be larger than zero, we want the Revenue (R) to be larger than the cost (C):

P = R - C

we want P > 0 (zero) then we want: R - C > 0 which means R > C

We can now replace R and C by their expressions in terms of x (the number of flags produced):

36 x > 32 x + 18695

we subtract 32 x from both sides to gather all terms in the variable "x" on the left hand side of the equation:

36 x - 32 x > 18695

4 x > 18695

Now we solve for x by dividing both sides by 4 (thus isolating the unknown x):

x > 18695 / 4

x > 4673.75

Therefore x must be at least the following integer to 4673.75, that is : 4674