Question

. A tech startup company has been monitoring its costs and revenue. The cost for each day, x, can be determined by the function C (x) = 3x 2 − 36x + 100, and their revenue by the function R(x)= −2x2 + 50x − 30. How many days will take for the company to earn profit?

Answer 1

The number of days it would take for the company to earn profit is approximately 16 days.

In Mathematics, profit is a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling x number of items can be calculated by using the following function:

Profit made = Revenue earned – Cost of production

P(x) = R(x) - C(x)

`P(x) = -2x^2 + 50x - 30 -(3x^2 - 36x + 100)\\\\P(x) = -2x^2 + 50x - 30 -3x^2 +36x - 100\\\\P(x) = -5x^2 + 86x - 130\\\\\\\x = (-b\; \pm \;√(b^2 - 4ac))/(2a)\\\\x = (-86\; \pm \;√(86^2 - 4(-5)(-130)))/(2(-5))`

x = 1.7 and x = 15.5

Since the company would begin to make profit when the revenue exceeds the cost, the number of days it would take for the company to earn profit is approximately 16 days.

Complete Question:

A tech startup company has been monitoring its costs and revenue. The cost for each day, x, can be determined by the function
`C (x) = 3x^2 - 36x + 100`, and their revenue by the function
`R(x)= -2x^2 + 50x - 30`. How many days will take for the company to earn profit?