APPLICATIONS
For Exercises 37–40, (a) select appropriate variables; (b) write the objective functions; (c) write the constraints as inequalities.
Business and Economics
40. Production Costs Cauchy Canners produces canned whole tomatoes and tomato sauce. This season, the company has available 3,000,000 kg of tomatoes for these two products. To meet the demands of regular customers, it must produce at least 80,000 kg of sauce and 800,000 kg of whole tomatoes. The cost per kilogram is $4 to produce canned whole tomatoes and $3.25 to produce tomato sauce. Labor agreements require that at least 110,000 person-hours be used. Each kilogram can of sauce requires 3 minutes for one worker, and each kilogram can of whole tomatoes requires 6 minutes for one worker. How many kilograms of tomatoes should Cauchy use for each product to minimize cost? (For simplicity, assume production of y1 kg of canned whole tomatoes and y2 kg of tomato sauce requires y1 + y2 kg of tomatoes.)
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Finite Mathematics and Calculus with Applications (10th Edition)
- Agriculture A fruit grower raises crops A and B. The yield is 300 bushels per acre for crop A and 500 bushels per acre for crop B. Research and available resources indicate the following constraints. β’ The fruit grower has 150 acres of land available. β’ It takes 1 day to trim the trees on an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days per year available for trimming. β’ It takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, and there are 30 days per year available for picking. What is the optimal acreage for each fruit? What is the optimal yield?arrow_forwardUse your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.arrow_forwardMaking furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80arrow_forward
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