A satellite TV company operating in the province is concerned that its profit level isn't as..

A satellite TV company operating in the province is concerned that its profit level isn’t as high as it should be. Presently it has $700,000 in fixed expenses every month. Program purchasing costs, maintenance costs and other operating costs bring the current level of variable costs to $32 per month in total. The current base of 30,000 customer pay $60 per month for the service. According to a recent market sensitivity analysis done for the company, it was determined that if the price was lowered/increased by $2 they would increase/decrease the number of customers by 3,000. This relationship between demand and price could be assumed to be linear over the relevant pricing range.

(a) What is the current monthly profit?

(b) Determine the demand equation.

(c) Give the function that gives the monthly profit as a function of the price.

(d) Determine the optimal price (omit the second order conditions), and calculate the number of customers and the monthly profit at this price.

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