2. An artisanal weaver makes two kinds of cloth: wool and cotton. Wool cloth can be sold for a profit of $3 per yard, and cotton cloth for a profit of $1 per yard. The weaver wants to maximize his profit He can afford to spend up to 40 hours per week working and takes two hours to make 1 yard of wool cloth and one hour to make 1 yard of cotton cloth. Customer demand requires that he makes at least three times as much cotton cloth as wool cloth. There is space for at most 100 yards of wool cloth cach week. the problem as a maximizing lincar program. Set b. Give the initial tableau for the problem. Find the optimal solution using the simplex method. Show your work. a. up C.
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- 4 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.1.A clockmaker makes two types of woodenclocksto sell at various malls. It takes him three hours to assemble a pine clock, which requires two oz of varnish. It takes four hours to assemblea molave clock, which takes four oz of varnish. He has eight oz of varnish available in stock and can work 12 hours. If he makes a P100 profit on each pine clock and P120 on each molave clock, how many of each type should he make to maximize his profit?2.A biologist is developing two new strains of bacteria. Each sample of Type A bacteria produces five new viable bacteria,and each Type B bacteria produces six new viable bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10, but not more than 20,of the original sample,must be Type A,and not more than 60 of the samples must be Type B. A sample of Type A costs P500,and a sample of Type B costs P700. If both types are to be used, how many samples of each type should be used to minimize the cost?Daisy Drugs manufactures two drugs: 1 and 2. Thedrugs are produced by blending two chemicals: 1 and 2. Byweight, drug 1 must contain at least 65% chemical 1, anddrug 2 must contain at least 55% chemical 1. Drug 1 sellsfor $6/oz, and drug 2 sells for $4/oz. Chemicals 1 and 2 canbe produced by one of two production processes. Runningprocess 1 for an hour requires 3 oz of raw material and 2hours skilled labor and yields 3 oz of each chemical.Running process 2 for an hour requires 2 oz of raw materialand 3 hours of skilled labor and yields 3 oz of chemical 1and 1 oz of chemical 2. A total of 120 hours of skilled laborand 100 oz of raw material are available. Formulate an LPthat can be used to maximize Daisy’s sales revenues
- A manufacturer can sell product 1 at a profit of $2/unitand product 2 at a profit of $5/unit. Three units of rawmaterial are needed to manufacture 1 unit of product 1, and6 units of raw material are needed to manufacture 1 unit ofproduct 2. A total of 120 units of raw material are available.If any of product 1 is produced, a setup cost of $10 isincurred, and if any of product 2 is produced, a setup costof $20 is incurred. Formulate an IP to maximize profits.Mr. Barrera raises goats and pigs. He wants to raise no more than 16 animals including no more than 10 goats. It will cost $25 to raise each goat and $75 to raise each pig. She will make $12 in profit from each goat and $40 in profit from each pig. She has $900 to raise animals. How many of each type of animal should she raise to maximize profit?2. A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans require 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earn $800 profit, and a lot of large-size cans earn $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can (and) in order to maximize profit. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
- United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a differentproduction capacity (in tons per day) for each grade, as follows:MillAluminumGrade 1 2High 6 2Medium 2 2Low 4 10The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5tons of low-grade aluminum. It costs United $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know thenumber of days to operate each mill in order to meet the contract at the minimum cost What would be the effect on the optimal solution if the cost of operating mill 1 increased from $6,000 to $7,500 per day?1. A town receives electricity generated from three forms of energy: solar, wind, tide. Consumer demand for electricity based on units of solar, wind, and tide is: Solar: 20 units, Wind: 30 units, Tide: 10 units. Internal Consumption: To convert one unit of solar requires: wind requires: tide requires: 0.4 units of solar 0.1 units of solar 0.3 units of solar 0.2 units of wind 0.3 units of wind 0.2 units of wind 0.1 units of tide 0.5 units of tide 0.1 units of tide S: Amount of solar supplied to meet the demands of the consumer and production (i.e., internal consumption). W: Amount of wind supplied to meet the demands of the consumer and production (i.e., internal consumption). T: Amount of tide supplied to meet the demands of the consumer and production (i.e., internal consumption). Write the three equations that represent the amount of each form of energy supplied to meet the demands of the consumer and production (i.e., internal consumption)Capsule Drugs manufactures two drugs. The drugs areproduced by blending two chemicals. By weight, drug 1must contain at least 65% chemical 1, and drug 2 mustcontain at least 55% chemical 1. Drug 1 sells for $6 perounce, and drug 2 sells for $4 per ounce. Chemicals 1and 2 can be produced by one of two production processes. Running process 1 for an hour requires 7 ouncesof raw material and 2 hours of skilled labor, and ityields 3 ounces of each chemical. Running process 2 foran hour requires 5 ounces of raw material and 3 hoursof skilled labor, and it yields 3 ounces of chemical 1 and1 ounce of chemical 2. A total of 3000 hours of skilledlabor and 5000 ounces of raw material are available.Determine how to maximize Capsule’s sales revenues.
- 2. A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 48 hours of labor and 120 units of lumber. Wren houses yield a profit of $10 each and bluebird houses yield a profit of $15 each. 1. The aim of the objective function for William should be to _______ a. Maximize b. Minimize the objective value. 2. a. Write out the objective and constraints. b. Solve graphicallyM&D Chemicals produces two products that are sold as raw materials to companies manufacturing bath soap and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, M&D’s management specifies that the combined production for products A and B must total at least 350 gallons. Separately, a major customer’s order for 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon, and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. M&D’s objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B. Develop a Linear Programming Model to determine how many gallons of each product should be produced. (using excel) please be detailed I need to understand how you you got each solution) 1) How many gallons of Product…A paper-making company has five machines that can produce four different types of papers. The company wants to assign each paper type to separate machines to minimize the total time required. The manufacturing times in minutes per unit of paper produced is listed below: Paper Type Machine Type A B C D M1 2.40 1.60 3.20 3.20 M2 2.10 2.40 3.20 4.50 M3 1.90 1.70 2.60 5.10 M4 2.50 2.50 3.20 6.50 M5 3.25 2.40 3.10 3.60 What is the optimal minimum time?