PLEASE ANSWER ALL THE QUESTIONS....

1.

A company is considering two insurance plans with coverage and Policy A Policy B premiums shown in the table. (For example, this means that $50 buys Fire/Theft $10,000 $15,000 one unit of plan A, consisting of $10,000 fire and theft insurance and $120,000 $180,000 of liability insurance.) Answer parts (a) and (b). Liability $180,000 Premium $50 $40 (a) The company needs at least $450,000 fire and theft insurance and at least $7,200,000 liability from these plans. How many units should be purchased from each plan to minimize the cost of the premiums? What is the minimum premium? The company should purchase units of Policy A and units of Policy B, for a premium of $A candy company has 114 kg of chocolate-covered nuts and 78 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. The other mix will contain nuts and Al - 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. The company should prepare kg of the first mix and kg of the second mix for a maximum revenue of $A patient takes vitamin pills. Each day he must have at least 840 IU of vitamin A, 4 mg of vitamin By, and 70 mg of vitamin C. He can choose between pill 1, which contains 300 IU of vitamin A, 1 mg of vitamin By, and 10 mg of vitamin C, and pill 2, which contains 120 IU of vitamin A, 1 mg of vitamin By, and 40 mg of vitamin C. Pill 1 costs 304, and pill 2 costs 150. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy of pill 1 and of pill 2. The minimum cost is $ (Simplify your answers. Type integers or decimals.)Adietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein: 3 units of carbohydrates. and 2 units of fat: and will contain 30 calories. Each ounce of nuts will supply 2 units of protein. 2 units of carbohydrates: and 4 units of fat. and will contain 4D calories. Every package must provide at least 2 units of protein: at least 3 units of carbohydrates. and no more than 12 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories? Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized? Z=|:|X+l:|y' A population gathers plants and animals for survival. They need at least 360 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 18 units of plants and 20 animals are available. It costs 20 hours of labor to gather one unit of a plant and 10 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. The population should gather units of plants and animals. (Simplify your answers.)(b) Suppose the premium for policy A is reduced to $25. Now how many units should be purchased from each plan to minimize the cost of the premiums? What is the minimum premium? The company should purchase units of Policy A and units of Policy B, for a premium of $(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. The company should prepare kg of the first mix and _kg of the second mix for a maximum revenue ofb. For the solution in part a. the patient is receiving more than he needs of at least one vitamin. ldentifv that vitamin. and tell how much surplus he is receiving. He is receiving . ILI of vitamin A. mg of vitamin E51. and mg of vitamin C more than he needs. [Simplify your answers] Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer loelow. K it Yes. Take one fewer of each pill to reduce the cost. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. Yes. Reverse the numbers of each pill taken. The dietician should use ounce(s) of fruit and ounce(s) of nuts. These amounts will have a total of calories. (Type whole numbers.)