Question 2

Cousin Brady has tried to analyze his business lines to find the optimal point of production. The supply function for their product is represented by the equation P=8Q + 200 and the demand function for a product line of a business is represented by the equation P=800-16Q.

i) sketch and Determine the equilibrium point of these equations. [5]

Cousin Brady hires an advertising company to help boost their sales and revenue. The advertising company relaunches their product line and is able to derive the following quadratic equation for the profit function .

Profit = -16t² + 48t + 100

ii) Assuming the profit is 0, solve the above equation to find the value of P. [4]

iii) Find the marginal profit. [4]