A manufacturer produces both widgets and gadgets. Widgets generate a profit of $25 each and gadgets have a profit margin of $75 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $300 for gadgets. Widgets consume 6 units of raw material A and 8 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 400 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution. The manufacturer will produce .......widgets and ...... gadgets the manufacturer's profit will be .....

A manufacturer produces both widgets and gadgets. Widgets generate a profit of $25 each and gadgets have a profit margin of $75 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $300 for gadgets. Widgets consume 6 units of raw material A and 8 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 400 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution. The manufacturer will produce .......widgets and ...... gadgets the manufacturer's profit will be .....

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 49P

See similar textbooks

Similar questions

In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?
A manufacturer produces both widgets and gadgets. Widgets generate a profit of $50 each and gadgets have a profit margin of $40 each. To produce each item, a setup cost is incurred. This setup cost is $300 for widgets and $400 for gadgets. Widgets consume 5 units of raw material A and 4 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 600 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution.
A manufacturer produces both widgets and gadgets. Widgets generate a profit of $70 each and gadgets have a profit margin of $45 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $500 for gadgets. Widgets consume 5 units of raw material A and 6 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 500 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets.Set up the problem in Excel and find the optimal solution. (Leave no cells blank — be certain to enter "0" wherever required. Round your answers to 2 decimal places.) (Round your answer to 2 decimal places.)
A glassblower makes glass decanters and glass trays on a weekly basis. Each item requires 1 pound of glass, and the glassblower has 15 pounds of glass available each week. A glass de- canter requires 4 hours of labor, a glass tray requires only 1 hour of labor, and the glassblower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is $10. The glassblower wants to determine the total number of decanters (x1) and trays (x2) that he needs to produce in order to maximize his profit. Requirements:a) Define decision variables and tabulated datab) Formulate the Integer Linear Programming Model.
A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution without integer restrictions and indicate whether the roundeddown solution would have been optimal.
Kevin runs a factory that makes stereo tuners. Each S100 takes 9 ounces of plastic and 6 ounces of metal. Each G150 requires 3 ounces of plastic and 9 ounces of metal. The factory has 360 ounces of plastic, 702 ounces of metal available, with a maximum of 24 S100 that can be built each week. If each S100 generates $13 in profit, and each G150 generates $8, how many of each of the stereo tuners should Kevin have the factory make each week to make the most profit? S100= G150= Best profit=
Formulate and then solve a linear programming model of this problem, to determine how manycontainers of each product to produce tomorrow to maximize profits. The company makes fourjuice products using orange, grapefruit, and pineapple juice.Product Retail Price per QuartOrange juice $1.00Grapefruit juice .90Pineapple juice .80All-in-One 1.10The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product isproduced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orangejuice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is$2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice.In addition, the manager wants grapefruit juice to be used for no more than 30 percent of thenumber of containers produced. She wants the ratio of the number of containers of orange juice tothe number of containers of pineapple juice to be at least 7 to 5.
A farm consists of 600 acres of land, of which 500 acres will be planted with corn, soybeans, and wheat, according to these conditions: At least half of the planted acreage should be in corn No more than 200 acres should be soybeans The ratio of corn to wheat planted should be 2:1 It costs $20 an acre to plant corn, $15 an acre to plant soybeans, and $12 an acre to plant wheat Formulate this problem as an LP model that will minimize planting cost while achieving the specified conditions.
You are working for Advance Technology, a company that produces three different devices for the military. The three devices that you produce are Main-bus Servo Modules, Secondary Trigger Activators, and Guidance Couplers. Advance Technology has two manufacturing facilities, the Croswell facility and the Grass Lake facility. Each day, the Croswell facility can produce 8 Main-bus Servo Modules, 4 Secondary Trigger Activators, and 4 Guidance Coupler at a cost of $1,800. Each day, the Grass Lake facility can produce 6 Main-bus Servo Modules, 12 Secondary Trigger Activators, and 2Guidance Couplers at a cost of $1,600. An order from the U.S. Navy for 210 Main-bus Servo Modules, 150 Secondary Trigger Activators, and 90 Guidance Couplers is received. Your boss has assigned to you the task of determining the number of days that each facility should operate to meet the order placed for the three devices at a minimum cost to your company.
A company manufactures plastic bottles, buckets, and cups. The profit units are $10 for a plastic bottle, $25 for a bucket,and 58 for a bag of cups. The machine that makes the goods has a capacity of 400 hours each month. The bottle takestwo hours to make, the bucket three hours, and the cup one hour. The company has a total of 890 units of plastic. Plasticbottles require three units, buckets five units, and cups one unit. In addition, there are 200 kg of a novel chemicalcomponent. This unique chemical component is employed in plastic bottles (2 kilogram), buckets (4 kg), and cups (0.5kg) . There is an order to produce only 50 bags of plastic cup. The company wants to find the optimal plan to maximizeprofit. Use the Simplex method to solve this problem.