Statistics and Probability

Use graphical metho to solve this linear programming problem, Minimize z = 5x+ By subject to: x yz 3 5x + 2y: 50 x20, y20 Use graphical methods to solve this linear Maximize 2 = 5x + 2y programming problem sublect to: 6x - y S16 3x + y 212 x23 y 59 A manufacturing company receives orders for engines from two assembly plants. Plant | needs at least 45 engines, and plant || needs at least 32 engines. The company can send at most 120 engines to these assembly plants. It costs $30 per engine to ship to plant land $40 per engine to ship to plant ll. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant || gives similar $10 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? A candy company has 189 kg of chocolate-covered nuts and 105 kg of chocolate-covered raisins to be sold as two different mixes. One mix will contain half nuts and half raisins and will sell for $7 per kg. 4 3 d1 Emilsan I. The other mix will contain raisins and will sell for $9.50 per kg. Complete parts a. and b. (a) How many kilograms of each mix should the company prepare for the maximum revenue? Find the maximum revenue. (b) The company raises the price of the second mix to $11 per kg. Now how many kilograms of each mix should the company prepare for the maximum revenue? Find the maximum revenue. A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from Dairy I costs $2.40 per gallon, and milk from Dairy It costs $0.00 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 55 gallons averaging 3.9% butterfat, and Dairy II can supply at most 80 gallons averaging 2.9% butterfat. Answer parts a and b. a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? b. The solution from part a leaves both Dairy l and Dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. A pension fund manager decides to invest a total of at most $35 million in U.S. Treasury bonds paying 5% annual interest and in mutual funds paying 7% annual interest. He plans to invest at least $5 million in bonds and at least $15 million in mutual funds. Bonds have an initial fee of $100 per million dollars, while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than $5000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest? A population gathers plants and animals for survival. They need at least 440 units of energy, 300 units of protein, and 8 hides. One unit of plants provides 30 units of energy, 10 units of protein, and 0 hides. One animal provides 20 units of energy, 25 units of protein, and 1 hide. Only 27 units of plants and 27 animals are available. It costs 20 hours of labor to gather one unit of a plant and 12 hours for an animal. Find how many units of plants and animals should be gathered to meet the requirements with a minimum number of hours of labor