A company's market research department is working on the pricing of a product. The product is one of 25 different products sold in a market, which currently yields half of the total profit. The field research shows that average demand is expected to be 8000 units at price 50 TL. Each 1 TL change in price is found to be negatively affecting the to the demand with a magnitude of 100 units. Fixed and variable costs are confronted for producing the product. According to the information obtained from the financial department 1.000.000 TL total fixed cost is confronted by the company 200,000 TL of which is incurred by the researched product. 20 TL is the estimate of variable costs per unit produced. Assume that all units produced are sold.

a) Sketch the graphs of corresponding total profit and marginal profit with respect to changes in price.

b) Determine the price that maximizes the company's profit.

c) What is domain and range of the demand function as a function of price?

d) Find the cost function.

e)Find revenue function as a function of price.

f) Find the profit function with respect to units sold.

g) Would you increase the price in order to increase total profit? Use price as independent variable of the function and justify your results.

h) Would you increase the price to 125 TL in order to increase total profit? Use price as independent variable of the function and justify your results.