Solve the following linear programming problem using simplex method. A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 of calories. Two foods A and B are available at a cost of Rs. 4 and Rs. 3 per unit respectively. If one unit of A contains 200 units of vitamins 1 unit of mineral and 40 calories and one unit of food B contains 100 units of vitamins, 2 units of minerals and 40 calories, find by simplex method what combination of Foods be used to have least cost.
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Solve the following linear programming problem using simplex method.
A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 of calories. Two foods A and B are available at a cost of Rs. 4 and Rs. 3 per unit respectively. If one unit of A contains 200 units of vitamins 1 unit of mineral and 40 calories and one unit of food B contains 100 units of vitamins, 2 units of minerals and 40 calories, find by simplex method what combination of Foods be used to have least cost.
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- SIMPLEX METHOD A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.Formulate a system of equations for the situation below and solve. Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 18%/year, while the bonds and the money market account pay 12%/year and 6%/year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. How should the Garcias allocate their resources if they require an annual income of $15,000 from their investments? stocks $ bonds $ money market $Company XYZ is a farming company. The company are famous for producing strawberries and blueberries. The variable cost of producing and selling one box of strawberries is $3, while the variable cost of producing and selling one box blueberries is $5. Each box of strawberries is selling for $10, while a box of blueberries sells for $13. The company produces and sells 5 boxes of strawberries for every 2 boxes of blueberries. Assuming a fixed cost of ?$204,000. How many boxes of blueberries need to be produced and sold to achieve breakeven 20,000 a O 8,000 b O 1,600 .c O None of the given answers d O 4,000 .e O
- Please answer it immediately sir Linear Programming The Booboo sawmill in Batangas produces pine and oak boards for manufacturing firms. Each month the sawmill must deliver atleast 5 tons of wood to the manufacturer . It takes the sawmill 3 days to produce a ton of pine and a 2 days to produce a ton of oak and the sawmill can allocate 18 days out of a month for this contract. The sawmill can get enough pine to make atleast 4 tons of wood and enough oak to make atmost 7 tons of wood. Determine the number of tons of pine and oak in order to minimize cost, given that pine has a cost of $3 and oak $6 to produce4) A printing company makes three grades of wall posters. The better-quality posters sell for Rs. 2.50, intermediate quality for Rs.2.00 and the poorer quality poster for Rs. 1.50. Paper costs Rs. 0.75 for each of the better-quality posters and Rs.0.50 and Rs. 0.25 for each intermediate and poorer quality poster respectively. Because of poor quality paper, the less expensive posters require two minutes of printing time while the other two require 1 minute of printing time only. The department is allocated Rs.150 per day for paper. There are 480 minutes of printing time available daily and each minute that is used to estimate to cost the company Rs. 0.25. In addition, the department incurs a fixed daily cost of Rs. 125, which are not affected by the quantity and quality of papers produced. You are asked to suggest as to how much each type of posters is to produce in order to maximize daily profit?(Don't use excel shortcut solve manually by Simplex LPP method)Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table. Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces. Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit. Decision Variables: X1 : number of basic tables to be produced. X2 : number of elegant tables to be produced. X3 : number of basic chairs to be produced. X4 :number of elegant chairs to be produced. Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit) Subject to 0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood) 2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000…
- standard mix of Peanut/Raisin Delite to put up. The deluxe mix has .68 pounds of raisins and .32 pounds of peanuts, and the standard mix has 0.5 pounds of raisins and 0.5 pounds of peanuts per bag. The shop has 80 pounds of raisins and 50 pounds of peanuts to work with. Peanuts cost $0.75 per pound and raisins cost $1.5 per pound. The deluxe mix will sell for $2.9 for a one-pound bag, and the standard mix will sell for $2.55 for a one-pound bag. The owner estimates that no more than 110 bags of one type can be sold. a. If the goal is to maximize profits, how many bags of each type should be prepared? (Round your answers down to a whole number.) Deluxe Standard b. What is the expected profit? (Round your answer to two decimal places.) Expected profitGeorgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final…Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 47 40 27 Hours required to complete all the cherry cabinets 64 51 36 Hours available 40 30 35 Cost per hour $34 $41 $52 For example, Cabinetmaker 1 estimates it will take 47 hours to complete all the oak cabinets and 64 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final…
- c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Explain. ✓ because Cabinetmaker 1 has dual value Yes ✓ of No -1.84 ✔ ✓ of Therefore, each additional hour of time for cabinetmaker 1 will reduce total cost by $ d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Use a minus sign to indicate the negative figure. Explain. ✔ because Cabinetmaker 2 has a slack 1.84 ✔ per hour, up to a maximum of 30 X hours. Alternatively, the dual value is 50 ✓ hours. 0.00 ✓ which means that adding one hour to this constraint will decrease total cost by $ 0.00 ✓.Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Hours required to complete all the oak cabinets Hours required to complete. all the cherry cabinets Hours available Cost per hour Min s.t. 01 Let O₁ O₂ 01 01 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.8, or 80%,…Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final…