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Show all your work, unsupported answers will receive no credit. Use correct mathematical notation at all times, points will be deducted for incorrect notation. Write your answers to applied problems in complete sentence form being specific about quantities and units. 1. A company manufactures and sells x television sets per month. The monthly cost and price-demand equation are C(x) = 72,000 + 60x p = 200- X 30 a) Write the Revenue and Profit functions, and determine their domain. b) Sketch a careful graph of the Revenue and Cost functions (the domain of the functions must be clearly indicated on the graph). On the graphs, indicate where the break-even points are and the production levels (values of x) that result in profit, and the ones that result in loss. r2. Optimization problem The average cost per unit when producing x units of a commodity is given by the equation 0.25x2+4_x+100 C(x) = ocstooo X where C (x) is in dollars. Find the production level that will minimize the average cost and determine the minimum average cost. Verify that what you found is indeed a minimum Write your answer in full sentence form specifying the values of all the variables in the problem and including appropriate units. 3. Optimization problem The Transit Authority (TA) in a metropolitan area operates a subway line that currently carries an average of 6000 passengers per day commuting between the suburbs and downtown. The fare new is $3.00 per ride and the board of the TA is considering raising its price by $0.50 to genomic a larger revenue. A study reveals that for each $0.50 increase in fare, the ridership will be reduced by an average of I000 passengers per day. Using this study, the board determines that, to get maximum prot, the price of the ticket should remain at $3.00. Is this correct? Explain why or why not. Show ALL your work to support your answer 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product and that the daily sales of the product (in thousands of dollars) are given by the following equation ${x)=x3212+4x8 05156 when x thousand dollars is spent on advertising [5 there a point of diminishing returns in this situation? If so1 determine what is the amount of money spent on advertising that corresponds to the point of diminishing returns and explain what that means