Widgetco produces widgets at plant 1 and plant 2. Itcosts 20x1/2 to produce x units at plant 1 and 40x1/3 toproduce x units at plant 2. Each plant can produce as manyas 70 units. Each unit produced can be sold for $10. Atmost, 120 widgets can be sold. Formulate an NLP whosesolution will tell Widgetco how to maximize profit.
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Widgetco produces widgets at plant 1 and plant 2. It
costs 20x1/2 to produce x units at plant 1 and 40x1/3 to
produce x units at plant 2. Each plant can produce as many
as 70 units. Each unit produced can be sold for $10. At
most, 120 widgets can be sold. Formulate an NLP whose
solution will tell Widgetco how to maximize profit.
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- A manager wants to know how many units of each product to produce on a daily basis in order toachieve the highest contribution to profit. Production requirements for the products are shown inthe following table.ProductMaterial 1(pounds)Material 2(pounds)Labor(hours)A 2 3 3.2B 1 5 1.5C 6 — 2.0Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product Asells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Availableresources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not bemore than one-third of the total number of units produced; the ratio of units of product A to units ofproduct B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solveFor a table manufacturing company, selling price for a table is $183.00 per Unit, Variable cost is $25.00 per Unit, rent is $3,380.00 per month and insurance is $296.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $254.00 per Unit, Variable cost to $43.00 per Unit, bigger area will have rent $5,235.00 per month and insurance is $362.00 per month At what point will the company be indifferent between the current mode of operation and the new option?Can you show how to put it in Excel? XYZ store sells regular and premium nut mixes. Premium mix contains three quarters pound of cashews and one quarter of peanuts, and the regular mix has half pound of cashews and half pound peanuts per bag. The shop has 200 pounds of cashews and 300 pounds of peanuts to work with. Cashews cost $1.50 per pound, and peanuts cost 60 cents per pound. Premium mix will sell for $2.90 per pound, and the standard mix will sell for $2.55 per pound. The owner esimtes that no more than 200 bags of one types can be sold. What is the best combinations of products that maximizes profits? Make sure to create a feasible solution with countable number of products (no partials)
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- A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?b. What is the maximum price the store would be justified in paying for additional pine bark?c. What is the marginal value of labor? Over what range is this value in effect?d. The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?e. If the manager can obtain either additional pine bark or additional storage space, which oneshould she choose and how much (assuming…A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.
- Steve's Scooer plans to sell it standard scooter for $500 and it chrome for $650. Steve purchases the standard scooter for $150 and Chrome for $250. Steve expects to sell one standard scooter for every three chrome scooter. Steve's monthly fixed cost are $263000. How many of each scooter must Steve sell each month to break even? and how many of each scooter must Steve sell each month to earn $697000?A. Write a document with the following information: 1. What do you expect your job to pay when you start? 2. What benefits are musts for you? 3. What benefits would you like to have even though they are not musts? 4. Include the graph you generate in step B below. B. Create a spreadsheet and a graph of life vs funds For each year of your remaining life specify the amount you plan to save/invest/withdraw that year and how much you expect that amount to increase during the year (base on actual data – typical savings interest rate, typical stock market interest rate, typical CDs, typical…). Calculate how much your funds will increase/decrease over your life and create a life (x-axis) vs funds (y-axis) plot.An electronics firm has a contract to deliver thefollowing number of radios during the next three months;month 1, 200 radios; month 2, 300 radios; month 3, 300radios. For each radio produced during months 1 and 2, a$10 variable cost is incurred; for each radio produced duringmonth 3, a $12 variable cost is incurred. The inventory costis $1.50 for each radio in stock at the end of a month. Thecost of setting up for production during a month is $250. Radios made during a month may be used to meet demandfor that month or any future month. Assume that productionduring each month must be a multiple of 100. Given thatthe initial inventory level is 0 units, use dynamicprogramming to determine an optimal production schedule.