Question

Q#4: Acme produces widgets. They have fixed monthly expenses of $1200 and also have variable expenses of $12 for each widget Acme sells each widget for $24. A) find cost function B) Revenue function C) Profit function.​

Answer 1

Answer:

A) $C_{x}=1200+12x$

B) $R_x=24x$

C) $P_x=100(x-100)$

Step-by-step explanation:

Let $x$ denote the number of widgets sold in a month.

Then, for a given month,

The cost function:

Cost= (Fixed monthly expenses) + (Variable Expense)*(Number of widgets)

Therefore, the cost as a function of number of widgets is given as;

$C_{x}=1200+12*x\\C_{x}=1200+12x$

The Revenue function:

Revenue=(Selling Price)*(Number of Widgets Sold)

Therefore, Revenue as a function of number of widgets is given as;

$R_{x}=S.P*x\\R_{x}=24*x\\R(x)=24x$

The Profit function:

Profit is given as the difference between Revenue and Expenses

$P_{x}=R_{x}-C_{x}\\ P_{x}=24x-(1200+12x)\\P_{x}=24x-1200-12x\\P_{x}=12x-1200\\P_{x}=12(x-100)$