An operations planner, Lovell Bradley, is developing a sales and operations plan that involves back orders. The company's demand and production rates for the next four periods are as follows: Period 1 2 3 4 Demand 8,200 10,000 7,000 6,600 Production 8,000 8,000 8,000 7,600 Beginning inventory at the start of period 1 is 400 units. Calculate beginning inventory, end- ing inventory, average inventory, and the back order amount, if any, for each of the next four periods.
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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?
- StockCo is considering five investments. The net present value (NPV) and capital require-ments over the next two years are summarized as follows:Net Present Capital Requirements ($)Value ($) Year 1 Year 2Investment 1 4,000 2,500 1,000Investment 2 6,000 2,000 3,500Investment 3 10,000 6,500 2,500Investment 4 7,000 5,000 1,500Investment 5 2,500 1,000 1,000Capital funds available for year 1 and year 2 are $7,500 and $5,500 respectively. In addition,StockCo needs to satisfy the following requirements:•StockCo can invest in at most three investments.•Investment 2 or 3 must be invested but not both.•If Investments 1 and 5 must be invested, they must be invested simultaneously.•If StockCo invests in investment 2, they must also invest in investment 4.a) Formulate an Integer Programming that will maximize the NPV of Stockco from allinvestments.b) Solve the problem by using Excel Solver. Show the optimal solution and optimal value in your printouts.Finco has the following investments available:Investment A For each dollar invested at time 0, we receive $0.10 at time 1 and $1.30 at time 2. (Time 0 =now;time= 1 one year from now; and so on.)Investment B For each dollar invested at time 1, we receive $1.60 at time 2.Investment C For each dollar invested at time 2, we receive $1.20 at time 3.At any time, leftover cash may be invested in T-bills, whichpay 10% per year. At time 0, we have $100. At most, $50can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco’s cash onhand at time 3.A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…
- Accompany makes two products (1&2) each product requires time on two machines (A&B). specification for each product is as follows. Product1 product2 Processing time on Machine A (hrs/unit) 2 2 Processing time on Machine B (hrs/unit) 1 2 Material and labour cost ( ksh/unit) 14 15 Selling price (ksh/unit) 16 18 Maximum possible sale (units) 130 150 The amount of time available on machine A is 360 hours and on machine B is 260 hours. Formulate the linear programme which, when…develope a space matrix for macdonalds. Below are the instructions. The steps required to develop a SPACE Matrix are as follows: 1. Select a set of variables to define financial position (FP), competitive position (CP), stability position (SP), and industry position (IP). 2. Assign a numerical value ranging from +1 (worst) to +7 (best) to each of the variables that make up the FP and IP dimensions. Assign a numerical value ranging from -1 (best) to -7 (worst) to each of the variables that make up the SP and CP dimensions. On the FP and CP axes, make comparison to competitors. On the IP and SP axes, make comparison to other industries. 3. Compute an average score for FP, CP, IP, and SP by summing the values given to the variables of each dimension and then by dividing by the number of variables included in the respective dimension. 4. Plot the average scores for FP, IP, SP, and CP on the appropriate axis in the SPACE Matrix. 5. Add the two scores on the x-axis and plot the resultant…Ann and Ben are getting divorced and want todetermine how to divide their joint property: retirementaccount, home, summer cottage, investments, and miscellaneous assets. To begin, Ann and Ben are told to allocate100 total points to the assets. Their allocation is as shownin Table 69.Assuming that all assets are divisible (that is, a fractionof each asset may be given to each person), how should theassets be allocated? Two criteria should govern the asset allocation:Criteria 1 Each person should end up with the same number of points. This prevents Ann from envying Ben and Benfrom envying Ann.Criteria 2 The total number of points received by Ann andBen should be maximized.If assets could not be split between people, what problemarises? TAB LE 69PointsItem Ann’s Ben’sRetirement account 50 40Home 20 30Summer cottage 15 10Investments 10 10Miscellaneous 5 10
- You own wheat warehouse with capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table Month Selling price ($) Purchase prie ($) 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 The sequence of events during each month is as follows: a. You observe your initial stock of wheat. b. You can sell any amount of wheat up to your initial stock at the current month's selling price. c. You can buy(at the current month's buying price) as much wheat as you want, subject to the warehouse size imitation. Your goal is to formulate an LP that can be used to determine how to maximise the profit earned over the next 10 months and solve using Excel solver or AMPLGerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements areDay M T W Th F S SuRequirements 6 3 5 3 7 2 3Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have two consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S–Su pair in case of a tie.Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…