9/13/10 Southwest Hospital has an operating room used only for eye surgery. The annual cost of rent, heat, and electricity for the operating room and its equipment is $320,000 and the annual salaries for the people who staff the room total $450,000. Each surgery performed requires the use of $550 worth of medical supplies and drugs. To promote goodwill, every patient receives a bouquet of flowers the day after the surgery. In addition, one-third of the patients require dark glasses, which the hospital provides for free. It costs the hospital $20 for each bouquet and $27 for each pair of glasses. The hospital receives $3000 for each eye operation performed. 1. a.) Find the Cost function. Define your x-variable. b.) Find the Revenue function. c.) Use algebra to find the Profit function. d.) Use the TI or any graphing program to graph these three functions on one set of axes. You can download winplot for free our use the program in Excel. Copy the graph to your paper. You can print from you graphing calculator using the cable provided in the math lab. Your graph must contain a title, axis labels indicating title, unit, and scale, and a key or a label on each line. e.) Use algebra to find the break-even point. Interpret the meaning of this point in sentences that include the words cost, revenue, and profit. Make sure to give a reasonable answer by using whole numbers. Label the break-even point on your graph. 2. One of the nurses has just learned of a machine that will reduce the supplies needed for each surgery by $200 per patient. It can be leased for $85,000 annually. a.) Find the new Cost function if the hospital chooses to lease the machine. Define the xvariable. b.) Find the new Profit function. c.) Use algebra to find the new break-even point. d.) You must advise the hospital administrator on whether he/she should lease the machine. . Base your answer on the break even points calculated and the fact that Southwest averages 40 operations per month and expects that trend to continue into the future. Your analysis should consider, break-even points, marginal profit and total profit. Write your recommendation is a paragraph citing your analysis. It should be written in business language. 1 3. The following table gives the price and demand for a certain brand of calculator. Demand in hundreds Price in dollars 4 125 9 119 15 108 22 97 25 91 32 80 a. Find the linear demand function using regression in Excel or with your calculator. b. Report and interpret the slope of your demand function. c. Using your function find the price when the demand is zero. d. Using your function find the demand when the price is $100 algebraically. e. A supplier is willing to supply 800 calculators when the price is $36.80 and is willing to supply 1500 calculators when the price is $51.50. If the supply function is linear, find the supply function algebraically hundreds of calculators. letting x be f. Find the equilibrium point algebraically using your demand and supply functions. Interpret the meaning of this point in a sentence. g. Graph the supply and demand equations on the same set of axis with your graphing calculator or graphing utility. Copy the graph into your paper. Make sure you include a title, the scale, label the axes, and clearly label each function with the equation. h. Label the equilibrium point on your graph. i. Suppose the price of the calculator is now $40, predict what will happen to the price and explain why using supply and demand. 2