15. Krouscas Foods makes a special blend of oil that is popular in Greek cooking. They import oil from two vendors and blend it to ensure that the resulting product contains at least 40% olive oil, 20% sunflower oil, and at least 30% corn oil. Vendor 1 can provide an oil containing 50% olive oil, 10% sunflower oil, and 40% corn oil at a cost of $9 per gallon. Vendor 2 can provide an oil containing 20% olive oil, 60% sunflower oil, and 20% corn oil at a cost of $8 per gallon. If Krouscas wants to produce 30 gallons of its special blend of Greek cooking oil at minimum cost, how much oil should it buy from each vendor? a. Formulate an LP model for this problem. b. Sketch the feasible region for this problem. c. Find the optimal solution.
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- 1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.Q. The price of each item in a store is nonnegative. The store manager is only interested in rules of certain forms, using the constraints given below. For each of the following cases, identify the kinds of constraint they represent and briefly discuss how to mine such association rules using a constraint-based pattern.Containing items whose sum of the prices is less than $150.
- 3. Elana owns a consulting business that helps software companies market their services to school districts. She earns an average of $4635.7 for every contract one of her client companies signs with her help. In order to be able to run her business, she needs to cover $7,000/month (rent, licenses, etc.). The average costs associated with each contract are $1676.6. How many contracts must she facilitate each month in order to break even? a. -2.37 b. 2.37 c. 10966.14 d. 1.51 e. -1675.09 f. None of the other options.2. A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal is to maximize profit, what would be the appropriate objective function? Select one: a. Maximize profit Z = $10Y + $25Z b. Maximize profit Z = 0.25Y + 0.20Z c. Maximize profit Z = $40Y + $25Z d. Maximize profit Z = $50(Y + Z) e. Maximize profit Z = $30Y + $20Z1.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?
- Two plants supply three customers with medicalsupplies. The unit costs of shipping from the plants to thecustomers, along with the supplies and demands, are givenin Table 42. TAB LE 42ToFrom Customer 1 Customer 2 Customer 3 SupplyPlant 1 $55 $65 $80 35Plant 2 $10 $15 $25 50Demand 10 10 10 a The company’s goal is to minimize the cost of meeting customers’ demands. Find two optimal bfs for thistransportation problem.b Suppose that customer 2’s demand increased by oneunit. By how much would costs increase?Mo. Samsung produces semiconductor chips in South Korea, China, and the United States. Products using these chips are sold around the world and therefore Samsung sells them on every continent. Below is the available supply and demand for all locations with the associated shipping costs. Supply (in millions) Demand (in millions) South Korea – 2.5 China – 3.5 United States – 2.0 North America – 2.1 South America – 1.4 Europe – 1.2 Africa – 1.1 Asia – 2.3 Australia – 0.8 Shipping Costs North America South America Europe Africa Asia Australia South Korea $12 $14 $9 $7 $3 $13 China N/A $15 $10 $8 $5 $16 United States $4 $6 $11 $17 N/A $18 Ongoing trade tensions between the United States and China have resulted in a ban on imports/exports. Additionally, the United States can only supply North America with 1.5 million and Australia requires at least 500,000 from South Korea. Using all this information, determine the optimal solution to the problem.Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$6 Activity 1 3 0 30 23 17 $C$6 Activity 2 6 0 40 50 10 $D$6 Activity 3 0 –7 20 7 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $E$2 Resource A 20 7.78 20 10 12.5 $E$3 Resource B 30 6 30 50 10 $E$4 Resource C 18 0 40 1E+30 22 What is the optimal objective function value for this problem?
- Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…23 The Northwest Flower Company owns a greenhouse, which furnishes roses and carnations to florists in Oregon, Washington, and Idaho. The greenhouse can grow any combination of the two flowers. They sell the flowers in "bunches" with 25 blooms to a bunch. They have 10,000 square feet available for planting this year. Each bunch of roses takes about 4 square feet and each bunch of carnations about 5 square feet. Special fertilizer is required for flowers: roses need 5 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 5000 pounds. Sales commitments require the company to grow at least 500 bunches of roses. Profit contributions are $6 per bunch of roses and $8 per bunch of carnations. a. Formulate this problem as an LP. b. Graph this problem. c. What are the corner points of the feasible region. d. What is the optimal solution? Please take a picture of all your hand writings and the detail of your work and upload here. Upload all…1. GIven the table below: Seattle California Las Vegas New Jersey supply Chicago $13 $12 $15 $10 1200 New York $11 $8 $25 $20 1375 Houston $4 $18 $10 $25 896 Georgia $8 $21 $12 $30 600 Kentucky $15 $6 $18 $20 459 Warehouse demand 1000 980 957 1593 a) use the NORTH WEST CORNER RULE model, create a transportation schedule that ensures that the supplies meet the warehouses’ demands b) determine the total transportation cost to the company in doing so.