Question: The price-demand equation and the cost function for the production of television sets are given, respectively, by \(p=300-\frac{x}{30}\) and \(C(x)=150,000+30x\), \(0\le x\le 9000\), where x is the number of sets that can be sold at a price of $p per set and C(x) is the total cost in dollars of producing x sets.

a. Find the revenue and profit functions in terms of x.

b. Determine the break-even points.

c. Find the interval(s) on which profit is increasing and decreasing, and determine any relative extrema in the profit.

d. Find \({P}'(4000)\text{ and }{P}'(7000)\) and interpret the results.

e. Determine the price elasticity of demand when the price is set at $120 per lawnmower and at $200 per television sets, and interpret the results.