A company that makes wooden tables and chairs has its production process with two basic types of labor: carpentry and finishing. Atable requires 2hours of carpentry and 1 hour of finishing, and a chair requires 3 hours of carpentry and hour of finishing. The profit is $35 per table and $20 per chair. *tThe employees can supply a maximum of 108 hours of carpentry work and 20 hours of finishing work per day. How many chairs must be made tomaximize profit.

It is provided that the item T requires 2 hours of carpentry and 1 hour of finishing. It is provided…

Answered: A company that makes wooden tables and…

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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Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 208 grams of protein and at least 178 grams of fat. If chicken costs 11¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost?
A fish farmer will purchase no more than 5000 young trout and bass from the hatchery and will feed them a special diet for the next year. The cost of food per fish will be $0.50 for trout and $0.75 for bass, and the total cost is not to exceed $3000. At the end of the year, a typical trout will weigh 3 pounds, and a bass will weigh 4 pounds. How many fish of each type should be stocked in the pond in order to maximize the total number of pounds of fish at the end of the year?
A farmer has 20 hectares for growing barley and swedes. The farmer has to decide how much of each to grow. The cost per hectare for barley is $30 and for swedes is $20. The farmer has budgeted $480. Barley requires I man-day per hectare and swedes require 2 man-days per hectare. There are 36 man-days available. The profit on barley is $100 per hectare and on swedes is $120 per hectare. Determine the number of hectares of each crop the farmer should sow to maximize the profits. Use GNU Octave to determine the maximization value as well as the point at which the maximum occurs.
Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 238 grams of protein and at least 158 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? grain ___oz chicken ____oz
Philippine Airlines (PAL) is considering air service from its hub of operations in Cicely, Alaska, to Rome, Wisconsin, and Seattle, Washington. PAL has one gate at the Cicely Airport, which operates 12 hours per day. Each flight requires 1 hour of gate time. Each flight to Rome consumes 15 hours of pilot crew time and is expected to produce a profit of $2,500. Serving Seattle uses 10 hours of pilot crew time per flight and will result in a profit of $2,000 per flight. Pilot crew labor is limited to 150 hours per day. The market for service to Rome is limited to nine flights per day. a. Use the graphic method of linear programming to maximize profits for Philippine Airlines. b. Identify positive slack and surplus variables, if any.
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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
Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super- Fit takes 12 minutes to cut and 30 minutes to sew and finish. Each pair of Super-Hug takes 12 minutes to cut and 40 minutes to sew and finish. The plant has enough workers to provide at most 12,599 minutes per day for cutting and at most 37,999 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $6.00 and the profit on each pair of Super-Hug is $7.00. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. (Use x for Super-Fit and y for Super-Hug.) Maximize P = < 12,599 ≤37,999 Maximum profit is $ subject to Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round jeans to 1 decimal place and profit to 2 decimal places. Number of Super-Fit jeans to…

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