Homework Answers
1)
Load of Assembly station = 100*10+200*5 = 2000 minutes
Load of Machine 1 = 100*7+200*8+2*240 = 2780 minutes
Load of Machine 2 = 100*5+200*(5+3)+2*30 = 2160 minutes
Load of Machine 3 = 100*22+200*0+90 = 2290 minutes
Load of Machine 4 = 100*10+200*10+60 = 3060 minutes
Load of Machine 4 is the highest. therefore, Machine 4 is the system constraint.
.
2)
Contribution margin of product X per minute of bottleneck time = (3000-500-500)/10 = $ 200
Contribution margin of product Y per minute of bottleneck time = (2000-500-100)/10 = $ 140
Production of products is prioritized in order of their contribution margin per minute of bottleneck time.
Therefore, product X is given first priority
Time available on bottleneck machine 4 after fulfilling demand of product X = 2400 - (100*10) - 60 = 1340 minutes
Quantity of product Y that can be produced in remaining time = 1340/10 = 134
Optimal product mix is:
Product X = 100 / wk
Product Y = 134 / wk
.
3)
Profit generated by the optimal product mix = 100*(3000-500-500)+134*(2000-500-100)-15000
= $ 372,600
.
4)
Utilization of each resource = Load / Capacity
Utilization of Assembly station = (100*10+134*5)/2400 = 69.6 %
Utilization of Machine 1 = (100*7+134*8+2*240)/2400 = 93.8 %
Utilization of Machine 2 = (100*5+134*(5+3)+2*30)/2400 = 68.0 %
Utilization of Machine 3 = (100*22+134*0+90)/2400 = 95.4 %
Utilization of Machine 4 = (100*10+134*10+60)/2400 = 100 %
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Problem 12 TOC PROBLEM GENERAL INFORMATION PRODUCT X S.P. = $3000 D= 100/WK PRODUCT Y S.P....
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Model GG $140 12 Model TS Selling price $100 Direct materials Direct labor ($12 per hour) 24 Variable support costs (S4 per machine-hour 8 Fixed support costs 20 Variable support costs are machine time at $4 per machine hour. Model AY $120 12 24 16 T 20 | T 48 1 6 20 Required: 1) Which model has the greatest contribution margin per unit? 2) Which model has the greatest contribution margin per machine-hour? 3) If the product mix is...
Question 4 - What is the best solution? Asmall farm makes the similar animal fodies Product Are Sho whour. O material 4 minutes of mixing using a mix-machine product requires 6 hours of w a l e s of mixing and productores 4 hours of labour, Skg of raw matal i king The firm has 210 hours available during the next period for labour. 200 kg of w e aland 170 forming Product contributes $28.00 per unit to profit, product...
5. What was the ratio of actual processing time for the product
to total lead time?
1075 International Journal of Prodiction Resecarch Project Management 90,60 30 days forecast End Customers Hyerson Steel Weekly Schedule Dally Shipping Schedule Welding Finishing Assembly Wiring Fabrication 23 days CIT-140.5mn PIT-250 min C/T 126min days CT-128min PIT-480 min CIT 120 Ave CIT 120 CIO 15 days 3 days 3 days 3 days 1 days L. T. 25 days 480 min 2400 min IP.T. 3158.5 min...
Note that in this part you are only asked to model the problem. Do NOT try to solve and find the optimal solution. In models if there are two many parameters or decisions variables, like in M4, you may use parametric modeling structure, like E ci Xi <Di for every j where Di demand-j cij cost at i-j Then give an example for j=1 this constraint is 12 X1 + 8 X2 <200. Where c11=12, c12=8 and Di= 200 with...
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