Data collected on the yearly demand for 50-pound bags of fertilizer at wallace garden supply areshown in the following table. develop a 3-year moving average to forecast sales. then estimate demandagain with a weighted moving average in which sales in the most recent year are given a weight of 2and sales in the other 2 years are each given a weight of 1. which method do you think is best? demand for fertilizeryear (1,000s of bags)1 42 63 44 55 106 87 78 99 1210 1411 15a)develop a trend line for the demand for fertilizer in problem 5-15, using any computer software. b) three different forecasts were developed for the demand for fertilizer. thesethree forecasts are a 3-year moving average, a weighted moving average, and a trend line. whichone would you use? explain your answer. c) use exponential smoothing with a smoothing constant of 0.3 to forecast the demand for fertilizergiven in question (a). assume that last period forecast for year 1 is 5,000 bags to begin the procedure. would you prefer to use the exponential smoothing model or the weighted average model developed in problem 5-15? explain your answer.

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.

Read the scenario. alfonso is 19 years old and has a high school diploma. recently, he was promoted to assistant manager at the fast-food restaurant where he has worked since the age of sixteen. his dream is to become the restaurant’s manager. what is his best option for achieving his dream? he should find another job and work his way up to a higher position. he should hope that his manager transfers to another location and that he is his replacement. he should attend classes at the local college to receive training in management. he should work hard, work longer hours, and remain assistant manager.