Question 3 Nomsa has found that the cost of running her salon is ZAR 8000 a year in fixed costs and variable costs of ZAR 120 per service provided. i) Determine the total cost per year for Nomsas salon and sketch the function. [4]

Nomsa decided to merge her salon with a few other salons in the area and they formed a company.

Below are the new total cost and total revenue functions for the new company:

Total Costs = 20Q2 + 2Q3 + 5000

Total Revenue= -0.5Q2 + 12Q + 10000

Given the above information answer the following questions:

ii. Calculate the marginal revenue and marginal costs. [4]

iii. Calculate the profit function and derive the marginal profit. [3]

iv. Calculate the breakeven point [2]

v. Determine total costs and total revenue when the quantity produced is 50 services [2]

vi. Nomsa's sister, Lindiwe has decided to also enter the beauty industry but will focus on luxury services. Assuming that her marginal cost of running a luxury salon is represented by the following function MC= 0.5x^2 .

What is the total cost function? [3]

vii. Define the limit and domain of a function. [2

Business statistics