An appliance manufacturer produces two models of televisions: colored tv and black & white tv. Both models require fabrications and assembly work; each colored tv uses four hours of fabrication and two hours of assembly, each black & white tv uses two hours of fabrication and six hours of assembly. There are 600 fabrication hours available per week and 480 hours of assembly. Each colored tv contributes P1200 to profits and each black & white tv contributes 900 to profits. How many colored tv and black & white tv must the manufacturer produce to maximize the profit. 1. Process Profit per unit OBJECTIVE FUNCTION: CONSTRAINTS: a. b. c. Non-negativity constraints= Coordinates Constraint a Let x=0 Constraint b. Let x=0 y = _ Lety-0 y=_ Let y = 0 X=> Determine the optimal solutions: Points Coordinates x= Hours per unit Sign Requirement Objective function equations Profits How many units of each brand must be produced to maximize profit? Determine the number of resources that will be used and the slack for each of the process. Constraints Used Available Slack

An appliance manufacturer produces two models of televisions: colored tv and black & white tv. Both models require fabrications and assembly work; each colored tv uses four hours of fabrication and two hours of assembly, each black & white tv uses two hours of fabrication and six hours of assembly. There are 600 fabrication hours available per week and 480 hours of assembly. Each colored tv contributes P1200 to profits and each black & white tv contributes 900 to profits. How many colored tv and black & white tv must the manufacturer produce to maximize the profit. 1. Process Profit per unit OBJECTIVE FUNCTION: CONSTRAINTS: a. b. c. Non-negativity constraints= Coordinates Constraint a Let x=0 Constraint b. Let x=0 y = _ Lety-0 y=_ Let y = 0 X=> Determine the optimal solutions: Points Coordinates x= Hours per unit Sign Requirement Objective function equations Profits How many units of each brand must be produced to maximize profit? Determine the number of resources that will be used and the slack for each of the process. Constraints Used Available Slack

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 1C

See similar textbooks

Similar questions

Hansen Controls has been awarded a contract for a large number of control panels. To meet this demand, it will use its existing plants in Houston and Tulsa, and consider new plants in Portland, St. Louis and Lexington. Finished control panels are to be shipped to Denver, Kansas City and Seattle. Pertinent information is given in the table. Denver 1 1- 2- 3- Sources 4- 5- Houston Tulsa Portland Construction St. Louis Cost Kansas City 2 ---- 1 Shipping Cost to Destination: Capacity Seattle 3 6 6 500,000 450,000 Lexington 400,000 Demand 14,000 13,000 18,000 We develop a transportation model as an LP that includes provisions for the fixed costs (construction costs in this case) for the three new plants. The solution of this model would reveal which plants to build and the optimal shipping schedule. Let xij = the number of panels shipped from source i to destination j y₁ = 1 if plant i is built, = 0 otherwise (i = 3, 4, 5) The constraint x21 + x22+x23 <= 13,000*y3 represents which of the…
Digital Controls, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time available and 1,080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time available at the Newark plant, DCI occasionally…
The following table provides a random sample of the unit values and annual demands of eight SKUs. SKU Code Unit Value Demand (units) A104 $0.02 D205 $2.60 X104 $4.80 U404 $2.50 L205 $0.36 S104 $0.84 X205 $4.35 L104 $0.23 4,500 30 25 2,500 1,040 380 70 250 Southern Markets Inc. is considering the use of ABC analysis to focus on the most critical SKUs in its inventory. a. Based on the percentage of dollar usage, which class should L205 belong to? Class b. Based on the percentage of dollar usage, which class should L104 belong to? Class
5. Meg Jones, the CEO of Ajax Computer Company, and Brad Smith, its Director of Operations, had been discussing how to increase the firm’s production of the company’s flagship XR58. The XR58 was particularly important because it sold 12,500 of them in the most recent year for $950, at a gross margin of 55%. After a lot of discussion, they decided to pursue an incentive system designed to increase production by 12% in the next year. After Brad discussed this possible incentive with the production team, the team determined that it could increase production by this amount without adding any more people or equipment. They believed they could accomplish this improvement primarily through process redesign. To incent them to do the hard work of process improvement, Brad told the team that it would receive 25% of the increased profits if it met the new production goal. For this team of 20 people, this would mean an additional compensation of _________ for each team member, on average, for…
How does the requirement that the number of units of model LX produced be at least 60% of the total production affect profits?
How does the requirement that the number of units of model LX produced be at least 60% of the total production affect profits? Show excel
Atlanta Manufacturing Company produces products W, X, Y, and Z through a joint process. The joint costs amount to $250,000. Product Units Produced Sales Value at Split-Off Additional Costs of Processing Sales Value After Processing W 750 $10,000 $2,500 $15,000 X 1,500 $30,000 $3,000 $35,000 Y 1,000 $20,000 $4,000 $25,000 Z 1,500 $40,000 $6,000 $45,000 If W is processed further, profits of W will: 1) Increase by $2,500 2) Increase by $12,500 3) Decrease by $23,000 4) Increase by $5,000
Sturgill Manufacturing Inc. needs to predict the numbers of machines and employees required to produce its planned production for the coming year. The plant runs three shifts continuously during the workweek, for a total of 120 hours of capacity per week. The shop efficiency (the percent of total time available for production), which accounts for setups, changeovers, and maintenance, averages 70% with a standard deviation of 5%, which reduces the weekly capacity. Six key parts are produced, and the plant has three different types of machines to produce each part. The machines are not interchangeable as they each have a specific function. The time to produce each part on each machine varies. The mean time and standard deviation (in hours) to produce each part on each machine are shown below: Mean Time Part Type Machine A Machine B Machine C 1 3.5 2.6 8.9 2 3.4 2.5 8 3 1.8 3.5 12.6 4 2.4 5.8 12.5 5 4.2 4.3 28 6…
Casting molds are produced by MYMOLD company. Each order has unique specifications, depending on customer needs. MYMOLD has received an order of two molds from a customer. The agreed selling price of the molds is 5000TL per mold. According to the agreement, for a defective mold the customer will pay 1000TL instead of the standard price. The customer will not buy any more than two molds and there is a 2000 TL fine for not meeting the demand with two non-defective molds. The excess molds can be salvaged for 500 TL per piece. The cost of production per mold is 2000TL and the probability of producing a non-defective mold is 0.8. Assume that MYMOLD decided to produce two molds, and the first production has been succesfull (a non-defective mold is produced). What is the expected profit given the result of the first production?
30) XYZ Company The XYZ Company uses 175 handles per day. The company operates 300 days per year. It costs $2.00 to carry one handle in inventory for one year. When handle inventory is low, an order is sent to the fabrication department to manufacture more handles. Fabrication can produce handles at a rate of 1500 per day and send the handles over to assembly while production is in progress. The setup for each production run costs $500. Assume the XYZ company orders 9,000 handles at a time (not necessarily the economic order quantity). The order receipt period = _____ days. Group of answer choices a) 6.0 b) 5.8 c) 30.0 d) 51.4 e) 50.0
Explain why multiple replications are needed when performing simulation analysis (Lean Manufacturing)
Cost Estimation; High-Low Method; MAPE Ethan Manufacturing Inc. produces floor matsfor automobiles. The owner, Joseph Ethan, has asked you to assist in estimating maintenancecosts. Together, you and Joseph determine that the single best cost driver for maintenancecosts is machine hours. These data are from the previous fiscal year for maintenance costs andmachine hours:Month Maintenance Costs Machine Hours1 $2,600 1,6902 2,760 1,7703 2,910 1,8504 3,020 1,8705 3,100 1,9006 3,070 1,8807 3,010 1,8608 2,850 1,8409 2,620 1,70010 2,220 1,10011 2,230 1,30012 2,450 1,590Required1. What is the cost equation for maintenance costs using the high-low method?2. Calculate the mean absolute percentage error (MAPE) for the cost equation you developed in requirement 1.