A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each ofnitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-lb bag of Fertilizer A costs $80and a 50-lb bag of Fertilizer B costs $70, find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements.Fertilizer AFertilizer BWhat is the minimum cost?$.2.022.bagsbagsMY NOTESASK YOUR TEACHERPRACTICE ANOTHER

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Answered: A farmer uses two types of fertilizers.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Darius runs a store that sells fancy chocolates. Each batch ofBlack Hole Dark Truffles takes 12 ounces of cocoa and 6 ounces of cream. Each batch ofMint Cream Breezes requires 54 ounces of cocoa, and 2 ounces of cream. The store needs to immediately use 972 ounces of cocoa and 336 ounces of cream. If each batch ofBlack Hole Dark Truffles costs $15 in expenses, and each batch ofMint Cream Breezes costs $16, we want to know how many of each of the fancy chocolates Darius should have the store make to have the least expenses.Which of the following are the constraint(s) in this situation? A. 12c+6c≥97212c+6c≥972 B. B≥15B≥15 C. E=15B+16ME=15B+16M D. M≥16M≥16 E. 54c+2c≥33654c+2c≥336 F. 15B+16M≥3115B+16M≥31 G. 12B+54M≥97212B+54M≥972 H. 6B+2M≥336
A farmer has 12 hectares of land on which he grows corn, wheat, and soybeans. It costs $4500 per hectare to grow corn, $6000 to grow wheat, and $5000 to grow soybeans. Because of market demand the farmer will grow twice as many hectares of wheat as corn. He has allocated $6,375,000.00 for the cost of growing his crops. How many hectares of each crop should he plant?
A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 75¢. 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 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2. (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. mg of vitamin C more than he needs. and He is receiving IU of vitamin A, mg of vitamin B₁, a (Simplify your answers.)
A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has 2/3 pound raisins and 1/3 pound peanuts, and the standard mix has 1/2 pound raisins and 1/2 pound peanuts per bagThe shop has 90 pounds of raisins and 60 pounds of peanuts to work with Peanuts cost $.60 per pound and raisins cost $1.50 per pound. The deluxe mix will sell for $3.60 for a on pound bag, and the standard mix will sell for $3.15 for a one-pound bagThe owner estimates that no more than 170 bags of or type can be sold
A patient takes vitamin pills. Each day he must have at least 300IU of vitamin A, 3 mg of vitamin B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B1, and 40 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 50¢. 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 nothing of pill 1 and nothing of pill 2. The minimum cost is $ nothing. (Simplify your answers. Type integers or decimals.)
A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 36 pounds of phosphoric acid, 30 pounds of nitrogen, and 6 pounds of potash. Each cubic yard of mix B contains 9 pounds of phosphoric acid, 30 pounds of nitrogen, and 36 pounds of potash. The minimum monthly requirements are 540 pounds of phosphoric acid, 900 pounds of nitrogen, and 360 pounds of potash. Find the set of feasible solutions graphically for the amounts of mix A and mix B that can be used.
.
An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10¢. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X2 S1 S2 S3 2.5 1 4.5 3 10 10
both sheets are for the same problem.

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