the following amounts represent the cost for producing a par

the following amounts represent the cost for producing a particular item. assume the cost function for producing x items is linear. find the cost function, revenue function and profit function

Fixed Cost =$15,000

Marginal Cost per item $9.5

Item Sells for $35

What is the cost function? C(x)=

What is the revenue function R(x)=

What is the profit function P(x)=

Solution

Total cost = Fixed cost + variable cost

Fixed cost = 15,000

Variable cost = 9.5 per item produced

Let the amount of goods produced and sold be x

Thus, Cost function C(x) = 15000 + 9.5x

Revenue function = amount sold * price per item

R(x) = 35x

Thus,

Profit = Revenue - cost

= 35x - (15000 + 9.5x)

= 25.5 x - 15000

Hope this helps.