Please answer all of the questions from the document and please the answers, while showing all work, in an EXCEL spreadsheet.
NAME____________________ 1. A service has five tasks, performed in sequence. In the instance when there is more than one worker assigned to a task, each worker performs the entire task and they both can be working on different “items” at the same time. Task Task time per worker Number of workers 1 2 minutes 1 2 6 minutes 1 3 14 minutes 2 4 4 minutes 1 5 15 minutes 3 a. What is the capacity (hourly) of the process as a whole? b. What is the bottleneck of the process? c. What is the throughput time (assuming no wait time)? d. Where would you expect customers to wait? 2. Artie Siegel, an MBA student, has been having problems balancing his checkbook. His monthly income is derived from a graduate research assistantship; however, he also makes extra money in most months by tutoring undergraduates in their quantitative analysis course. His historical chances of various income levels are shown in the following table: Monthly Income* ($) Probability 350 0.40 400 0.20 450 0.30 500 0.10 *Assume that this income is received at the beginning of each month. Siegel’s expenditures also vary from month to month, and he estimates that they will follow this distribution: Monthly Expenses ($) Probability 300 0.10 400 0.45 500 0.30 600 0.15 He begins his final year with $600 in his checking account. Simulate the entire year (12 months) on the next page and discuss Siegel’s financial picture, i.e., will he be able to keep his head above water--(out of debt)? What is his expected average profit for the 12 months? Use the random numbers below. Random numbers for Income and Expenses Income 85 54 73 95 9 19 81 2 76 55 57 1 Expenses 99 44 1 80 95 72 75 16 32 57 31 32 3. Hands-on is a company that features a product line of winter gloves for the entire family— men, women, and children. They want to decide what mix of these three types of gloves to produce. The Hands-on’s manufacturing labor force is unionized. Each full-time employee works a 40-hour week. In addition, by union contract, the number of full-time employees can never drop below 20. Nonunion, part-time workers also can be hired with the following union-imposed restrictions: (1) Each part-time worker works 20 hours per week, and; (2) There must be at least two full-time employees for each part-time employee. In terms of the manufacturing process, all three types of gloves are made out of the same 100 percent genuine cowhide leather. Hands-on has a long-term contract with a supplier of the leather and receives a 5,000 square-foot shipment of material each week. The material requirements and labor requirements, along with the gross profit per glove sold (Not considering labor costs), are given in the following table below: Glove Material Required (Square Feet) Labor Required (Minutes) Gross Profit (per pair of gloves) Men’s 2 30 $8 Women’s 1.5 45 10 Children’s 1 40 6 Each full-time employee earns $13 per hour, while each part-time employee earns $10 per hour. Management wishes to know what mix of each of the three types of gloves to produce per week, as well as how many full-time and part-time workers to employ while they would like to maximize their net profit—their gross profit from sales minus their labor costs. Formulate a linear programming model to determine the best mix of gloves and employees to have to maxmize their net profit. (DO NOT attempt to solve.) Briefly identify/describe each decision variable, constraint and objective function. 4. HBK, a food industry company wants to build a forecasting model to predict the sales of its hot-beverage. HBK had the last weekly sales for the past 152 weeks. Using the time series components for trend (variable called tp) and seasonal--monthly dummy variables (using Dec as a baseline) and the causal variable of average weekly temperature HBK management build the model on the following page. Note the average hot-beverage weekly sales is $91,500. a. Evaluate the model on the following page, i.e., is it a good model? If so, why, or if not, why? Consider all the appropriate tests, use α = 0.05 for t test and α = 0.05 for F test. Notice on the following page is a plot of the residuals. DO ALL APPROPRIATE TESTS--COMPLETELY!!!! b. If you believe the model is OKAY, provide at least two reasons to justify your belief. On the other hand, if you believe the model is not OKAY, provide suggestions on how you would improve the model. c. Ranking the order of the months in terms of their impact on weekly sales, i.e., which month has the highest expected weekly sales, next highest, and which are the lowest and second lowest? Highest 1 2 3 4 5 6 7 8 9 10 11 12 Lowest HIGHEST_________________ NEXT HIGHEST _________________ * * SECOND LOWEST_________________ LOWEST_________________ (d). Show how you will code the dummy variables in this model, in other words fill in 13 rows with your dummy variables in the table below. (the first column, Month, tells you what month it is). Month Jan Feb Mar Apr May Jun July Aug Sept Oct Nov Dec Jan (e). What is the model’s predicted value or forecast for time period 20, which is August, and the average monthly temperature is 80? 5. The Ace Manufacturing Company produces two lines of its product, the super and the regular. Resource requirements for production are given in the Table below. There are 1,600 hours of assembly worker hours available per week, 700 hours of paint time, and 300 hours of inspection time. Regular customers will demand at least 150 units of regular line and 90 of the super. Product line Profit Contribution Assembly time (hr.) Paint time (hr.) Inspection time (hr.) Regular $50 1.2 .8 .2 Super $75 1.6 .9 .2 The linear programming formulation for this product mix problem is: Decision variables x1 = units of regular produced x2 = units of super produced Formulation Maximize Z = 50x1 + 75x2 s.t. 1.2x1 + 1.6x2 ≤ 1600 Assembly time .8x1 + .9x2 ≤ 700 Paint time .2x1 + .2x2 ≤ 300 Inspection time x1 ≥ 150 Regular demand x2 ≥ 90 Super demand x1, x2 ≥ 0 Answer the following questions on this page and the next page referring to the above formulation and the printout on the page following the questions a. What is the optimal solution (complete answer!)? b. If demand for regular increased by 10, what will happen to the optimal solution (Z and decision variables)? c. If demand for super increased by 10, what will happen to the optimal solution (Z and decision variables)? d. If the profit contribution of regular decreased to 30, what will happen to the optimal solution (Z and decision variables)? e. If the profit contribution of super decreased to 55, what will happen to the optimal solution (Z and decision variables)? Residuals-15023.599068558718-9595.37822024263015449.1629929143819-26688.605876740655312.0655351409814-13830.02950718643833725.29072911607440032.99512821558935976.582835444962-28588.25268308195542932.77162089597648263.854082558566-7522.757833621813918100.112066353064-88033.12110096024117887.091027872419103328.57879667202-77767.21495634818-30432.2249550659336809.6939567445661-34181.568029578943-57666.30216655528112547.996745222999829.6819410056778-32827.195889820825844.441552602482264037.958034412760810245.2613398228869278.11537811639573650.31546864879783557.7523144190054-2728.1979024141256-1468.0616378630075-4204.52125127772623973.8541024728643-7369.3182102346618-5672.78168313438075215.8327127616094-5812.0000987893145-11312.322766834732335.78130720847139-9219.70840261419651539.1390999755968-2529.6402146770051-9267.0192658621891-7869.3234965435131-486.34988105654378-5819.6915215306717-364.5411987865225-39845.114192382862-24098.304797619166-34038.591351402429-15319.03703516253223759.024814469914-25567.0771817930224186.9959683522484-9682.66876299039-24220.728989318275-4718.767243816226377562.610445732571692.9889845550066-3869.8469749055221-11750.40662634485530493.7009658673635053.3214946138951-364.27893995202561-19076.118466472166-6492.66649146140356946.151709616708-13927.651928065025-44304.79136671483913702.4514797505438759.48275852933942352.703477388735-18918.06688611417513639.54307990647110315.94989445617510251.5173445361529044.72984011811793852.6967587692343-5818.8847187465535-701.46982942771808-4877.86717314170161537.39302964055246871.2668515559117-794.41273287602291-1021.3760527920234983.02193914640523826.1113384475866-2882.4971382936956-4388.0682224573175-14420.083708392467-2618.0339424407211-10465.188643437647-1291.4555132167998-3965.6659337504402-8335.9306125666662-1017.8917270594175-8498.5288091155891338.653021481776-6421.93932018162745825.1604082025151-27069.895647271216-19150.967355214034-28491.13957014029815936.520945918208-7367.3098367430212-23798.1184864192919470.322689631335462696.154465483225-9950.14377812393477052.951150125417421984.7349408119922425.8026118179259-5744.533274306682938075.02438175497810624.974260004156550.7044224992014-28657.34999875206337.5264160611259574539.82704617080349672.1532831123968-13783.30331460420529089.49151503490130049.8836865181-8370.539245894389820953.01751565326422926.1105797952621079.577605294325610371.9513701706469717.20576787625213144.6953808359772-4313.16255045453-722.24410130621982-3712.16856739044319782.09742508982897934.62242260291535767.5997201458704-8988.6920556770492-5408.0594333580084-2147.4063293837899-6723.5588412543293-7061.5653923366299-2560.0543905839022-4452.1292283028861-9872.0302929784702-10984.530268533177-2679.125596055761-2636.4540700960715-11767.4826581958372652.3494390248998time period SUMMARY OUTPUT Regression Statistics Multiple R 0.938986698 R Square 0.881696019 Adjusted R Square 0.870551442 Standard Error 24568.19214 Observations 152 ANOVA df SS MS F Significance F Regression 13 6.21E+11 4.78E+10 79.11435 3.1962E-57 Residual 138 8.33E+10 6.04E+08 Total 151 7.04E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 310087.8302 16946.59 18.29795 1.01E-38 276579.255 343596.4 276579.3 343596.4 Avg Wkly Temp -3061.992316 422.168 -7.25302 2.66E-11 -3896.747343 -2227.24 -3896.75 -2227.24 tp -121.7295379 48.8318