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1- Mack’s guitar fabrication shop produces low cost, highly durable guitars for beginners. Typically, out of the 100 guitars that begin production each month, only 80 percent are considered good enough to sell. The other 20 percent are scrapped due to quality problems that are identified after they have completed the production process. Each guitar sells for $250. Because some of the production process is automated, each guitar only requires 10 labor hours. Each employee works an average of 160 hours per month. Labor is paid at $10/hour, materials cost is $40/guitar, and overhead is $4,000. a) Calculate the labor and multifactor productivity ratio. b) After some study, the operations manager recommends 3 options to improve the company’s multifactor productivity: (1) increase the sales price by 10 percent, (2) improve quality so that only 10 percent are defective, or (3) reduce labor, material, and overhead costs by 10 percent. Which option has the greatest impact on the multifactor productivity measure? Calculate the labor and multifactor productivity ratio. 100/160=0,625 (250*80) / [(160*10)+(40*100)+4000] = 20000/9600=2,08 After some study, the operations manager recommends 3 options to improve the company’s multifactor productivity: (1) increase the sales price by 10 percent, (2) improve quality so that only 10 percent are defective, or (3) reduce labor, material, and overhead costs by 10 percent. Which option has the greatest impact on the multifactor productivity measure? 1-250*0,10=25 new sales price=250+25=275 (275*80) / [(160*10)+(40*100)+4000] =2,29 2-(250*90) / [(160*10)+(40*100)+4000] =2,34 3-[(160*9)+(36*100)+3600] =8640 new total cost (250*80) /8640 =2,31 Second option has the greatest impact on the multifactor productivity measure. 2- Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 of B.To meet customer demands, at least 10 units of A, 5 of B, and 3 of C must be produced daily. Graphically determine a daily production plan that minimizes the cost of meeting Leary Chemical’s daily demands. A 3 1 >= 10 PROCESS1 PROCESS2 PRODUCT B 1 1 >= 5 C 1 >= 3 Min z= 4*x1 +1*x2 s.t 3x1+x2 >=10 x1+x2>=5 x1>=3 x1,x2 >=0 3x1+x2 =10 3x1+x2=10 x1=3,33 x2=0 x1=0 x2=10 x1+x2=5 x1=3 x1=5 x2=0 x1=0 x2=5 x1=3 for point A x1+x2=5 x1=3 so x1=3 x2=1 X2 10 5 2,5 A 2 1 B 2,5 3 3,5 5 A,B, points are feasible points. A(3,2); B(5,0) Minimum cost for point; Z=4x1+x2 A(3,2); 4*3+2=14 (optimal point) B(5,0); 4*5+0=20 X1 3- Jenny Lind is a writer of romance novels. A movie company and a TV network both want exclusive rights to one of her more popular works. If she signs with the network, she will receive a single lump sum, but if she signs with the movie company, the amount she will receive depends on the market response to her movie. What should she do? Payouts and Probabilities Movie company Payouts Small box office - $200,000 Medium box office - $1,000,000 Large box office - $3,000,000 TV Network Payout Flat rate - $900,000 Probabilities P(Small Box Office) = 0.3 P(Medium Box Office) = 0.6 P(Large Box Office) = 0.1 4- A manufacturer with four production locations wishes to minimize the shipping cost to their four warehouses. The supply from each factory and the demand of each warehouse are shown in the table along with the cost to ship one unit from each factory to each warehouse. Factory A B C D Total Demand Warehouse Warehouse Warehouse Warehouse Total 1 2 3 4 Supply $5 $6 $4 $7 250 $8 $3 $7 $4 150 $6 $4 $5 $6 300 $7 $3 $4 $2 250 300 200 150 300 What is the lowest total cost for the factories to supply the warehouses with Northwest model and VAM ? According to Vogel’s Approximation Model(VAM) 1.rule; find the difference between lowest two cost values in every columns and rows 2.rule;define the highest difference and choose the lowest cost in its column or row 3.rule begin with that cell