Profit A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are
Find the number of each type of product that should be manufactured to maximize profit. What is the maximum profit?
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Chapter 14 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- Nutrition A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 32 units of niacin and 22000 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.12 unit of niacin and 100 units of retinol per gram. Food B contains 0.20 unit of niacin and 50 units of retinol per gram. How many gram of each food does she feed this group of rats each day?arrow_forwardChemistry A chemist needs 10 liters of a 25 acid solution. The solution is to be mixed from three solutions whose concentrations are 10,20,and50. How many liters of each solution will satisfy each condition? (a) Use 2 liters of the 50 solution. (b) Use as little as possible of the 50 solution. (c) Use as much as possible of the 50 solution.arrow_forwardNutrition A doctor recommends that a patient take 50 mg each of niacin, riboflavin, and thiamin daily to alleviate a vitamin deficiency. In his medicine chest at home the patient finds three brands of vitamin pills. The amounts of the relevant vitamins per pill are given in the table. How many pills of each type should he take every day to get 50 mg of each vitamin?arrow_forward
- Gas Station A gas station sells three types of gas: Regular for 3.00 a gallon, Performance Plus for 3.20 a gallon, and Premium for 3.30 a gallon. On a particular day 6500 gallons of gas were sold for a total of 20,050. Three times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day?arrow_forwardAPPLICATIONS Classroom UseA small school has 100 students who occupy three classrooms: A, B. and C. After the first period of the school day, half the students in room A move to room B, one- fifth of the students in room B move to room C, and one-third of the students in room C move to room A. Nevertheless, the total number of students in each room is the same for both periods. How many students occupy each room?arrow_forwardAPPLICATIONS Manufacturing FurnitureA furniture factory makes wooden tables, chairs, and armoires. Each piece of furniture requires three operation: cutting the wood, assembling, and finishing. Each operation requires the number of hours given in the table. The workers in the factory can provide 300 h of cutting. 400 h or assembling, and 590 h of finishing each work week. How many tables, chairs, and armoires should he produced so that all available labor-hours are used? Or is this impossible? Table Chair Armoire Cutting h 12 1 1 Assembling h 12 112 1 Finishing h 1 112 2arrow_forward
- Mixing Feed A milling company wants to mix alfalfa which contain 20 protein, and wheat mids,38 which contains 15 protein, to make cattle feed. a. If you make a mixture of 30 pounds of alfalfa and 40 pounds of wheat mids, how many pounds of protein are in the mixture Hint: In the 30 pounds of alfalfa, there are 300.2=6 pounds of protein. b. Write a formula that gives the amount of protein in a mixture of a pounds of alfalfa and w pounds of wheat mids. c. Suppose the milling company wants to make 1000 pounds of cattle feed that contains 17 protein. How many pounds of alfalfa and how many pounds of wheat mids must be used?arrow_forwardAPPLICATIONS AgricultureA farmer has 1200 acres of land on which he grows corn, wheat, and soybeans. It costs 45 per acre to grow corn, 60 to grow wheat, and 50 to grow soybeans. Because of market demand, the farmer will grow twice as many acres of wheat as of corn. He has allocated 63,750 for the cost of growing his crops. How many acres of each crop should he plant.arrow_forwardNutrition A researcher performs an experiment to test a hypothesis is that involves the nutrients niacin and retinol. She feeds one group of laboratory rats daily of diet of precisely 32units of niacin and 22,000units of retinol. She uses two types of commercial foods. Food A contains 0.12unit of niacin and 100units of retinol per gram. Food B contains 0.20unit of niacin and 50units units of retinol per gram. How many grams of each does she feed this group of rats each day?arrow_forward
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