Managerial Science Final Exam 8w

10) (8 pointsA storm insurance center receives calls from people in need of counsel at a rate of 13 calls/hour. T a)Probability that no calls are in the system b)Average number of calls on hold (waiting) c)Average waiting time per caller d)Average service time (combined) e)Probability a new calls is not answered immediately 11) (8 points 12) (8 points A financial advising office welcomes an average of 1.8 customers per hour at its retail office. It take calculate all Operating Characteristics metrics for this office. Suffolk County Court House has just installed a new sercurity protocol for visitors. Three body scan can process 12 visitors per minute. Tuesdays have been identified as being the least busy with an a scanners are operating on Tuesday, compute the Operating Characteristics for this court house. (M to your Excel file)

The center can serve 15 calls/hour. Assuming Poisson distribution of calls and exponential distribution for the es 13 minutes on average per customer to provide financial advice. Assuming Poisson arrivals and exponentia nners have been installed at the entrance. There is not need to have both machines staffed all day long every average of just 10 visitors per minute. Assume Poisson arrival and exponential distribution for the scanner. If Make sure you use my file to compute this one as it requires special formulation. You can later copy the results

Zone Downtown Financial 1, 2, 5, 6 Downtown Legal 2, 4, 5 Retail South 1, 2, 4, 6 Retail East 3, 4, 5 Manufacturing North 1, 2, 5 Manufacturing East 3, 4 a. Develop Corporate West 1, 2, 6 Min t.r. X1 + X2 + X3 + X4 + X5 + X6 X1+X2+X5+X6 >= 2 X2+X4+X5 >= 2 X1+X2+X4+X6 >= 2 X3+X4+X5 >= 2 X1+X2+X5 >= 2 X3+X4 >= 2 X1+X2+X6 >= 2 Locations Variables X1 X2 X3 X4 X5 Min Coefficients 1 1 1 1 1 1 1 1 1 0 Z= 4 Locations Zones X1 X2 X3 X4 X5 Downtown Financial 1 1 1 Downtown Legal 1 1 1 Retail South 1 1 1 Retail East 1 1 1 Manufacturing North 1 1 1 Manufacturing East 1 1 Corporate West 1 1 Zones Downtown Financial 2 >= 2 Downtown Legal 2 >= 2 Your express package courier company is drawing up new zones for the location of drop boxes for cu The list of which drop boxes could be reached easily from each zone is listed below.Let xi = 1 if drop zone is covered by at least two boxes. Save your work in Tab #13 Can Be Served By Locations:

ns for drop boxes. ke sure that each

w product estate xpansion is selected, it will also modernize its current facilities. x1= New Product R&D x2= Plant Expansion x3= Modernization x4= Real Estate 5.2X1 + 3.6X2 + 3.2X3 + 2.8X4 <= 0.85 x1(0.35)+x2(0.50)+x3(0.35)+x4(0.50) <= 0.85 <= 1.00 x1(0.55)+x2(0.50)+x3(0.40) <= 1.00 ears to be $850,000, $1,000,000, and $1,200,000, respectively. It is considering four options for the dis ng year's investment in the projects. The expected benefits three years hence from each of the four pr

3(10) Project 1 2 Engineers Required 20 55 Support Personnel Required 15 45 Profit ($1,000,000s) 1 1.8 Formulate an integer LP that maximizes Tower's profit in Tab #15 subject to the follo 1) Use no more than 175 engineers 2) Use no more than 150 support personnel 3) If either project 6 or project 4 is done, both must b 4) Project 2 can be done only if project 1 is done 5) If project 5 is done, project 3 must not be done an 6) No more than three projects are to be done. Max x1(1.0)+x2(1.8)+x3(2.0)+x4(1.5)+x5(3.6)+x6(2.2) x1(20)+x2(55)+x3(47)+x4(38)+x5(90)+x6(63) <= 175 x1(15)+x2(45)+x3(50)+x4(40)+x5(70)+x6(70) <= 150 x4-x6 <= 0 x6-x4 = 0 x2-x1 <= 0 x5+x3 <= 1 x1+x2+x3+x4+x5+x6 <= 3 Variables X1 X2 X3 X4 Coefficients 1.0 1.8 2.0 1.5 0 1 0 1 Z= 3.30 X1 X2 X3 X4 Constraint 1 20 55 47 38 Constraint 2 15 45 50 40 Constraint 3 1 Constraint 4 -1 Constraint 5 -1 1 Constraint 6 1 Tower Engineering Corporation is considering undertaking several proposed projects expected profits for each project are summarized in the following table:

1 1 <= 3 x1+x2+x3+x4+x5+x6 <= 3

for each project, and the

4) (7 points Economic Order Quantity 4,000 =D Ordering Cost $15.00 =Co Annual Inventory Holding Rate 0.2 =I Cost per Unit $10.00 =C Working Days per Year 275 Lead Time (Days) 5 =L Optimal Inventory Policy Economic Order Quanity (EOQ) 244.95 =SQRT(2*B3*B4)/(B5*B6)) Holding Cost per Unit $2.00 =B5*B6 Annual Inventory Holding Cost $244.95 =(1/2)*B13*(B5*B6) Annual Ordering Cost $244.95 =(B3/B13)*B4 Total Annual Cost (TC) $489.90 =B15+B16 Maximum Inventory Level 244.95 =B13 Average Inventory Level 122.47 =B18/2 Reorder Point 72.73 =(B3/B7)*B8 Number of Orders per Year 16.33 =B3/B13 Cycle Time (Days) 16.84 =B7/B20 Southern Fields grows avocados faces a constant demand of 4,000 cases per year. Each case of avoc Reorder Point, Cycle Time, and Total annual cost. Annual Demand

cados has a $10 cost for the company. It costs $15 to fullfill an order and 20% holding cost. This company is o

open for business 275 days/year with a lead time of 5 days. Calculate EOQ,

5) (7 points) Economic Order Quantity 30,000 Ordering Cost $32.00 Annual Inventory Holding Ra 0.05 Cost per Unit $7.00 Working Days per Year 360 Lead Time (Days) 10 Optimal Inventory Policy Economic Order Quanity (EOQ) 2,342.16 Holding Cost per Unit $0.35 Annual Inventory Holding Cost $409.88 Annual Ordering Cost $409.88 Total Annual Cost (TC) $819.76 Maximum Inventory Level 2,342.16 Average Inventory Level 1171.08 Reorder Point 833.33 Number of Orders per Year 12.81 Cycle Time (Days) 28.11 Anran Inc. produces microchips f Calculate EOQ, Reorder Point, Cy Annual Demand

=D =Co =I =C =L =SQRT(2*B3*B4)/(B5*B6)) =B5*B6 =(1/2)*B13*(B5*B6) =(B3/B13)*B4 =B15+B16 =B13 =B18/2 =(B3/B7)*B8 =B3/B13 =B7/B20 for cellphone makers at a constant rate. It requires 2,500 parts/month production per year. With an orderin ycle Time, and Total annual cost.

ng cost of $32 and $7 per part, it faces a low holding cost of 5% and 10 days of lead time. This facility runs 36

60 days per year.

6) (8 points) Economic Production Lot Size 100,000 Annual Production Rate 125,000 Setup Cost $5,000.00 Annual Inventory Holding Rate % 0.12 Cost per Unit $1.20 Working Days per Year 250 Lead Time (Days) 12 Optimal Inventory Policy Production Lot Size 186,339 Annual Inventory Holding Cost $2,683.28 Annual Setup Cost $2,683.28 Total Annual Cost $5,366.56 Maximum Inventory Level 37,267.80 Average Inventory Level 18633.90 Reorder Point 4800.00 Number of Orders per Year (Cycles) 0.54 Cycle Time (Days) 465.85 Length of Production 465.85 Length of Idle 0.00 Production Utilization 100.0% Alba Inc, manufactures LED equipment. Demand for this ty run Vesper Inc spends $5,000 in setup cost. The firms is cap calculate Min cost of production, number of productions p Annual Demand

ype of lights takes place at a constant rate of 100,000 per year. Manufacturing cost at $1.20 per unit and it co pable of producing 125,000 units per year and operate 250 days per year. Lead time for a production run is cu per year, cycle time, length of each production run, Max inventory, total annual cost, and reorder point.

osts 12% to hold in inventory. After each production urrently at 12 days. Using Production Lot Size Model,

Anran Inc (problem 5) has decided to switch to a backorder inventory policy. The firms estimates $7 backorder co Economic Order Quantity with Planned Shortages 30,000 Ordering Cost $32.00 Annual Inventory Holding Rate % 0.05 Cost per Unit $7.00 Annual Backorder Cost per Unit 7 Working Days per Year 360 Lead Time (Days) 10 Optimal Inventory Policy Economic Order Quanity (EOQ) Q* 23427.46 Number of Backorders 11.71 Annual Inventory Holding Cost $40.96 Annual Ordering Cost $40.98 Annual Backorder Cost $0.02 Total Annual Cost $81.96 Maximum Inventory Level 23,415.75 Average Inventory Level 11702.02 Reorder Point 821.63 Number of Orders per Year 1.28 Cycle Time (Days) 281.13 Annual Demand

ost. Calculate Min cost order quantity, Max number of backorders, Max inventory, cycle time, and total annua

l cost.

1,000 Probability that there will be a zero inventory is 0.00 Zharassova Imports is planning to import t-shirts for a sports event. The shirts are printed with a one of the wins it will be forced to discount them and sell them for $10. Each shirt costs $15 to import. Assuming a a n optimal order quantity and what is the probability that Zharassova will have zero inventory after the event?

possible winners. The company expects to sell the shirts for $30 before the event, but if the oponent team normal distribution for sales with a mean m=100,000 and a standard dev. σ=1,200, what would be the

A storm insurance center receives calls from people in need of counsel at a rate of 13 calls/hour. The center a)Probability that no calls are in the system 0.133 b)Average number of calls on hold (waiting) 2.82 c)Average waiting time per caller 13 minutes d)Average service time (combined) 17 minutes e)Probability a new calls is not answered immediately 0.87

r can serve 15 calls/hour. Assuming Poisson distribution of calls and exponential distribution for the for the se

ervice, calculate the following:

A financial advising office welcomes an average of 1.8 customers per hour at its retail office. It takes 13 minu calculate all Operating Characteristics metrics for this office.

utes on average per customer to provide financial advice. Assuming Poisson arrivals and exponential service ti

times,

Suffolk County Court House has just installed a new sercurity protocol for visitors. Three body scan can process 12 visitors per minute. Tuesdays have been identified as being the least busy with an scanners are operating on Tuesday, compute the Operating Characteristics for this court house. (M to your Excel file)

nners have been installed at the entrance. There is not need to have both machines staffed all day long ever n average of just 10 visitors per minute. Assume Poisson arrival and exponential distribution for the scanner. If Make sure you use my file to compute this one as it requires special formulation. You can later copy the result

ry day. Each scanner f only just two ts from my template