A poultry producer wants to mix corn meal and soybean meal so as to provide his chickens with a diet that minimizes cost subject to three nutritional re quirements. Corn meal costs $0.10/lb and soybean meal costs $0.20/lb. The diet should provide each chicken with at least 6 units of nutrient U, 4 units of nutrient V, and 6 units of nutrient W. A pound of corn meal provides 3 units of nutrient U, 1 unit of nutrient V, and 1 unit of nutrient W. A pound of soybean meal provides 1 unit of nutrient U, 1 unit of nutrient V, and 3 units of nutrient W. The cheapest nutritionally adequate diet for a chicken costs
A poultry producer wants to mix corn meal and soybean meal so as to provide his chickens with a diet that minimizes cost subject to three nutritional re quirements. Corn meal costs $0.10/lb and soybean meal costs $0.20/lb. The diet should provide each chicken with at least 6 units of nutrient U, 4 units of nutrient V, and 6 units of nutrient W. A pound of corn meal provides 3 units of nutrient U, 1 unit of nutrient V, and 1 unit of nutrient W. A pound of soybean meal provides 1 unit of nutrient U, 1 unit of nutrient V, and 3 units of nutrient W. The cheapest nutritionally adequate diet for a chicken costs
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:31. A poultry producer wants to mix corn meal and soybean meal so as to provide
his chickens with a diet that minimizes cost subject to three nutritional re
quirements. Corn meal costs $0.10/lb and soybean meal costs $0.20/lb. The
diet should provide each chicken with at least 6 units of nutrient U, 4 units of
nutrient V, and 6 units of nutrient W. A pound of corn meal provides 3 units
of nutrient U, 1 unit of nutrient V, and 1 unit of nutrient W. A pound of
soybean meal provides 1 unit of nutrient U, 1 unit of nutrient V, and 3 units
of nutrient W. The cheapest nutritionally adequate diet for a chicken costs
(а) $.25
(b) $.31
(c) $.38
(d) $.45
(е) $.50
Expert Solution
Step 1
This is a minimization problem.
Let the cheapest nutritionally adequate diet consist of c pounds of corn meal and s pounds of soybean meal. Then, the cost of a diet is
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