Mathematical Methods for Business and Economics by Edward T. Dowling

Author:Edward T. Dowling
Language: eng
Format: epub
Publisher: McGraw-Hill
Published: 1993-08-23T16:00:00+00:00

x1 + x2 + 3x3 ≤ 4

x1, x2, x3, ≥ 0

(a)

2x1 + x2 + x3 + s1 = 2

x1 + x2 + 3x3 + s2 = 4

In matrix form,

(b) With v = 5 and n = 2, 5 − 2 = 3 variables must be set equal to zero for a basic solution. Setting x1 = x2 = x3 = 0, the initial basic solution is s1 = 2 and s2 = 4.

7.23. Find the total number of basic solutions that exist in Problem 7.22.

Substituting v = 5 and n = 2 in the formula.

Supplementary Problems

MATHEMATICAL EXPRESSION OF BUSINESS AND ECONOMIC PROBLEMS

7.24. A bakery makes $4 profit on its wedding cakes x1 and $3 on its birthday cakes x2. Wedding cakes take 4 minutes for mixing, 90 minutes for baking, and 8 minutes for icing. Birthday cakes take 6 minutes for mixing, 15 minutes for baking, and 4 minutes for icing. The bakery has 120 minutes of mixing time, 900 minutes of baking time, and 96 minutes of icing time. Express the data in terms of equations and inequalities necessary to determine the combination of wedding cakes and birthday cakes that will maximize profit subject to the constraints.

7.25. A maker of fine preserves earns $15 profit on its premium brand x1 and $6 profit on its standard brand x2. The premium-brand preserves take 7.5 minutes for peeling, 20 minutes for stewing, and 8 minutes for canning. The standard-brand preserves take 5 minutes for peeling, 30 minutes for stewing, and 2 minutes for canning. The manufacturer has 150 minutes for peeling, 540 minutes for stewing, and 120 minutes for canning. Reduce the data to equations and inequalities suitable for finding the combination of brands that will maximize profit.

7.26. A cereal manufacturer wants to make a new brand of cereal combining two natural grains x1 and x2 The new cereal must have a minimum of 128 units of carbohydrates, 168 units of protein, and 120 units of fructose. Grain 1 has 24 units of carbohydrates, 14 units of protein, and 8 units of fructose. Grain 2 has 4 units of carbohydrates, 7 units of protein, and 32 units of fructose. Grain 1 costs $7 a bushel, grain 2 costs $2. Express the data in equations and inequalities amenable to finding the least-cost combination of grains that will fulfill all the nutritional requirements.

7.27. A landscaper wants to mix her own fertilizer containing a minimum of 50 units of phosphates, 240 units of nitrates, and 210 units of calcium. Brand 1 contains 1 unit of phosphates, 6 units of nitrates, and 15 units of calcium. Brand 2 contains 5 units of phosphates, 8 units of nitrates, and 6 units of calcium. Brand 1 costs $2.50 a pound; brand 2 costs $5. Express the data in equations and inequalities suitable to determine the least-cost combination of fertilizers that will meet her requirements.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.