(b) Develop the three-week moving average for this time series. (Round your answers to two decimal places.) Week Time Series Forecast Value 1 19 2 12 3 17 4 10 1.72 5 18 60 14 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (c) Use a = 0.2 to compute the exponential smoothing values for the time series. Week Time Series Forecast Value 1 19 2 12 3 17 4 st 10 5 18 10 6 14 Centerville Bikes and Stuff (CBS) sells motorcycles and accessories. The number of helmets sold by CBS per week for the past six weeks follows. Week 1 2 3 4 5 6 Value 19 12 17 10 18 14 (a) Construct a time series plot. 20 18 16 14 20 18 16 14 12 10 8. 20 18 20 T 16 18 14 16 12 14 10 12 10 8 2- 2 0 1 2 3 4 5 6 7 0 2 3 4 5 6 7 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Week Week Week Week What type of pattern exists in the data? The data appear to follow a seasonal pattern. The data appear to follow a horizontal pattern. The data appear to follow a cyclical pattern. The data appear to follow a trend pattern.
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- The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
- When you use a RISKSIMTABLE function for a decision variable, such as the order quantity in the Walton model, explain how this provides a fair comparison across the different values tested.You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the previous problem. Still another fairly simple trend line is the parabola, a polynomial of order 2 (also called a quadratic). For the demand-price data in the file P13_10.xlsx, fit all three of these types of trend lines to the data, and calculate the MAPE for each. Which provides the best fit? (Hint: Note that a polynomial of order 2 is still another of Excels Trend line options.)
- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?KrazySockzThe KrazySockz Company is known for their colorful yetcomfortable socks. They have forecasted their demand for the nextsix months as follows: Month 1 demand is 30,000, month 2demand is 50,000, month 3 demand is 20,000, month 4 demand is10,000, month 5 demand is 15,000 and month 6 demand is 20,000.At the beginning of month 1 they have 15,000 pairs of socks onhand. KrazySockz currently has 40 production employees. Each productionemployee costs the company the company $4,000 per month ($3,200 salary and $800in other costs) per month. Production employees can work up to 160 hours permonth before they must be paid overtime. Overtime is paid at a rate of $30 per hourand production employees can not work more than 30 hours per month overtime. Ittakes 15 minutes of labor and $0.75 of raw material to produce a pair of socks.KrazySockz can hire or fire employees each month. Hiring a production employeeincurs a cost of $3,500 and firing a production employee costs $4,500. At the end…
- Make a planning model for this question. A bank issues several financial products at the beginning of each month, and the corresponding expected rate of return and investment time (counted in months) of each product is different. A man holds $100000 of capital at the end of 2019 and planned to use this capital at the end of the year 2020. Make a planning model (linear programming) to help him decide how to buy the financial product.A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in ExcelThe management accountant at Miller Merchandising & More, Odail Russell is in the process of preparing the cash budget for the business for the fourth quarter of 2021. It is customary for the business to borrow money during this quarter. Extracts from the sales and purchases budgets are as follows: Month Cash Sales Sales On Account Purchases August $85,000 $640,000 $420,000 September $70,000 $550,000 $550,000 October $88,550 $600,000 $500,000 November $77,160 $800,000 $600,000 December $174,870 $500,000 $450,000 An analysis of the records shows that trade receivables are settled according to the following credit pattern, in accordance with the credit terms 4/30, n90: 50% in the month of sale 30% in the first month following the sale 20% in the second month following the sale Expected purchases include monthly cash purchases of 5%. All other purchases are on account. Accounts payable are settled as follows, in…