A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window. a. Define decision variables that will tell how many units to build (doors and windows) per week. b. Develop an objective function that will maximize total profit per week. c. Develop production constraints for work area #1 and #2.

A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window. a. Define decision variables that will tell how many units to build (doors and windows) per week. b. Develop an objective function that will maximize total profit per week. c. Develop production constraints for work area #1 and #2.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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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.
A manufacturing plant produces a product 'A' that requires one unit of 'B' and ½ unit of 'C'. Each unit of 'B' is comprised of one unit of 'D', two units of 'E', and one unit of 'F'. Each unit of 'C' requires ½ unit of 'G' and three units of 'H'. The manufacturing lead times for the components are as follows: 'A' - two weeks, 'B' - one week, 'C' - two weeks, 'D' - two weeks, 'E' - three weeks, 'F' - one week, 'G' - two weeks, 'H' - one week. There are 20 units in stock for each of these components. 100 units of 'A' are needed for delivery in seven weeks: a) Develop the product structure and indexed bill of materials for the product. b) Create a gross and net requirements plan for the manufacturer of the product.
Company ZWZ manufactures three products in a serial system; Product XA is manufactured in Stage 1, Product XB in Stage 2, and XC in Stage 3. Product XB has a sales potential in the market; hence, some of it can be sold at the end of Stage 2, and the remaining can be moved to Stage 3. The third stage produces Product XC, and then delivers it to customers. Two units of Product XA produced in Stage 1 are required for each unit of Product XB in Stage 2. In addition, four units of Product XB produced in Stage 2 are required for each unit of Product XC in Stage 3. Stage 1 can only use regular time; however, Stage 2 has the options of using regular time and overtime in manufacturing. On the other hand, Stage 3 has only one alternative, which is subcontracting. The pertinent data are provided below: Stage 2 Stage 1 11 No overtime No subcontracting No sales 0.07 Unit regular time cost (TL) Unit overtime cost (TL) Unit subcontracting cost (TL) Unit selling price (TL) Unit processing time (hrs)…
There is an upstream Picking department that feeds two downstream Packing departments: Pack Singles and Pack Multis. Those Packing departments feed to a Shipping department that loads the outgoing trucks. 40% of your Pick volume goes to Pack Singles and has a packing rate of 104 units per labor hour (uph). 60% of the Pick volume goes to Pack Multis and has a pack rate of 215 units per labor hour. Your pickers pick both Single and Multi items throughout the day at an overall average rate of 114 units per labor hour. All units that are packed in both processes go through the Ship process at a rate of 570 units per hour. You have 102 people today for all 4 departments and you absolutely must pack 47,880 units in Pack Multis Items to meet a customer promise metric. How do you allocate labor to balance the flow in your department if you work a 10 hour shift? Do not assume breaks or lunches in your answer. Redirect 1: You now need to process all of the Pack Singles Volume in the first 5…
Three methods can be used for producing heat sensors for high-temperature furnaces. Method A will have a fixed cost of $140,000 per year and a production cost of $62 per part. Method B will have a fixed cost of $210,000 per year and a production cost of $28 per part. Method C will require the purchase of equipment costing $500,000. It will have a life of five years and a 25% of first cost salvage value. The production cost will be $53 per part. At an interest rate of 10% per year, determine the breakeven annual production rate between the two lowest cost methods.
A machine part to be fabricated may be made from alloy of either of two metals. There is an order for 10,000 units. Metal A costs 3 pesos per kg, while Metal B costs 9 pesos per kg. If Metal A is used, the material per unit weighs 110 grams; for metal B, 30 grams. When metal A is used, 50 units can be produced per hour; for metal B, 80 units per hour. Metal B fabrication requires the aid of a tool costing P1,000, which will be useless after the 10,000 units are finished. The machine operator's wage is P50 per hour. If all other costs are identical, determine which material will be more economical to finish the 10,000-unit order. How much is the total cost difference between the use of metal A and metal B?
4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?
A custom motor cycle shop is experiencing high demand from its customers for its services. The owner performs all tasks relating to customization. Assume each customer brings one motor cycle for customization. The owner needs to determine if he needs to add more help to meet customer demand. A week has 40 hours ( maximum amount of time for the owner to work) The maximum number of customizations that can be done per week is 10 bikes ( if there is no wasted time). The following is the data collected from observations for a typical week : Every Friday the shop is cleaned by the owner. This takes 4 hours. - 15 % of the customizations needs rework which takes 50 % more time than regular customization - 10 % of the customers will be called by the owner. This takes 2 hours per customer. Determine OEE. How should the owner handle the business ? Show all formulas used, calculations and results. Do on Blk Bd For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
. A group of students organizes a bake sale in which they sell hundreds of cookies at $1per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables is an output variable?a. 3b. 4c. 5d. None of the above
Assuming your company is producing Apple and Samsung phone cases. It is required to process in the assembly and paint shops to make either phone case. It takes 1/60 of a day and 1/40 of a day to paint an Apple case and a Samsung case in the paint shop, respectively. It takes 1/50 of a day to assemble either type of case in the assembly shop. An Apple phone case and a Samsung phone case yield profits of $300 and $220, respectively, per case sold. What is a maximum-profit daily production plan for your company?
A Las Vegas, Nevada, manufacturer has the option to make or buy one of its component parts. The annual requirement is 20,000 units. A supplier is able to supply the parts for $10 per piece. The firm estimates that it costs $600 to prepare the contract with the supplier. To make the parts in-house, the firm must invest $50,000 in capital equipment, and the firm estimates that it costs $8 per piece to make the parts in-house. Assuming that cost is the only criterion, use breakeven analysis to determine whether the firm should make or buy the item. 1. What is the breakeven quantity? 2. Should the manufacturer Make or Buy? 3. What is the cost savings using your decision in number 2 (above)? Show the total cost for each scenario then the savings amount.
During an eight-hour shift, 750 non-defective parts are desired as a result of a manufacturing operation. The default operation time is 15 minutes. As the operators of machine are inexperienced, the actual time they take to perform the operation is 20 minutes, and, on average, a fifth of the parts that start to be manufactured are lost. Assuming that each one of the machines used in this operation will not be available for one hour in each shift, determine the number of machines needed.