The price of a belt 15 each If the fixed cost is 3000 and th

The price of a belt $15 each. If the fixed cost is $3000, and the total cost of 10 belts is $3100. Find the cost function C(x) where x is the number of belts.(Recall that the total cost is the sum of the fixed cost and the variable cost) Solution: C(x) = Find the revenue function R(x). Solution R(x) = How belts need to produced and sold in order to break even? Number of belts is: What\'s the marginal profit? Marginal profit =

Solution

For cost function we have : fixed cost $ 3000 with x =0

( 10 belts , $ 3100) and ( 0, 3100)

So, find the cost function from the above information : C(x)

slope = ( 3100 - 3000)/( 10 -0) = 10

C(x) = 10x + 3000    ---- Cost function

Revenue function : eachj belt sells for $ 15 each

R(x) = 15x

Break even : R(x) =C(x)

10x + 3000 = 15x

5x = 3000 ; x = 600 belts should be sold

Profit function : R(x) - C(x) = 10x + 3000 - 15x = 3000 - 5x

Marginal profit = derivatve of profit = -5