Four products are processed sequentially on three machines. The following table gives the pertinentdata of the problem.Manufacturing time (hr) per unitMachineCost of hrProduct 1Product 2Product 3Product 4Capacity($)10(hr)1234500232238034731450Unit Selling Price ($)75705545Formulate the problem and find the optimum solution. After solving the problem, please generatingSensitivity Report.What should happen, if the capacity of Machine 1 is increased to 550 hours?ANone of aboveBThe profit is increased by $165The profit is increased by $375DThe profit remains same

Find Solution using Voggel's Approximation method, also find optimal solution using modi method,…

Answered: Four products are processed…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
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LMNO Gaskets has formulated a production plan for a product to meet demand over the upcoming three quarters. Demand in each of the three quarters and production, overtime, and subcontracting capacities are reported in the table below, in addition to the feasible production plan. The relevant costs are: Regular time production cost is $25/unit. Overtime production cost is $32/unit. Subcontracting cost is $34/unit. Inventory is held at a cost of $3/unit/quarter. Units may be backordered at a cost of $5/unit/quarter. Production Resource Demand in Quarter Capacity Q1 Q2 Q3 Regular Time Q1 600 0 0 600 Overtime Q1 200 50 0 250 Subcontract Q1 0 0 0 500 Regular Time Q2 0 600 0 600 Overtime Q2 0 250 0 250 Subcontract Q2 0 490 10 500 Regular Time Q3 60 0 540 600 Overtime Q3 40 60 140 250 Subcontract Q3 0 0 0 500 Demand in Quarter 900 1450 690 What is the inventory cost for the year? What is the backorder cost for the year? What is the total overtime production…
Note: please do NOT use EXCEL
Smith Smith Products Ltd produces two products, in a process which is partly automated. It is restricted to 400 labour hours and 600 machine hours in the coming week. Information on each product is as follows: Per unit A B £ £ Selling price 50 60 Labour (£10 per hour) 20 30 Material used 8 12 Other variable costs 17 14 Fixed costs 3 1 Machine time taken 4 hours 2 hours Required: Derive the objective function Set out the constraints in a mathematical format Sketch a graph representing the problem; identify the feasible region and the optimal solution before solving algebraically for the optimal production plan.
Atlas Engineering Ltd. Accepts a variety of jobs which require both and machine operations. The budgeted Profit & Loss Account for the period 2018-19 is as follows: (in lakhs of dollars) Sales 75 Cost: Direct Material 10 Direct Labour 5 Prime Cost 15 Production Overheads 30 Production Cost 45 Administration, Selling and Distribution Overheads 15 60 Profit 15 Other budgeted data : Labour hours for the period 25,000 Machine hours for the period 15,000 No. Of jobs for the period 300 An enquiry has been received recently from a customer and the production department has prepared the following estimate of the prime cost required for the job : Direct Material $ 2,500 Direct Labour $ 2,000 Prime Cost $ 4,500 Labour hours required = 80 Machine hours required = 50 You are required to: (a) Calculate by the different methods, six absorption rates for absorption of production overhead and comment on the suitable of each. (b) Calculate the production overhead cost of the order based on each of the…
You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled a. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? b. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?

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