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.

mx+89b(-98)nb

step-by-step explanation:

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step-by-step explanation:

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