QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) 2 where x is previously defined, and c is total cost. A. Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i. E. Revenue = price × quantity] (3 marks) B. Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced] (3 marks) C. Find the profit function [Hint: profit is revenue minus total cost] (2 marks) D. Find the quantity that maximizes profit (2 marks)

(a)Revenue function,

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit,

(d)x=4

Step-by-step explanation:

Part A

Price Function

The revenue function

The marginal revenue function

Part B

(Fixed Cost)

The total cost function of the company is given by

We expand the expression

Therefore, the fixed cost is 900 .

Marginal Cost Function

If  

Marginal Cost Function,

Part C

Profit Function

Profit=Revenue -Total cost

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

The number of cakes that maximizes profit is 4.

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are