Problem 3 The Silly Nut Company makes two mixtures of nuts: Mixture A and Mixture B. A pound of Mixture A contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for 4 dollars. A pound of Mixture B contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for 15 dollars. The company has 1080 oz of peanuts, 240 oz of almonds, 160 oz of cashews. How many pounds of each of mixtures A and B should the company make to maximize profit? Variable Peanuts Almonds Cashews Price Mixture A 12 1 4 Mixture B 12 2 2 15 Inventory 1080 240 160 A. Decision variables Mixture A = X1 Мixture B - X2 B. Objective Function Maximize (z) = 4X1 + 15X2 C. Constraints peanuts = 12X1 + 12X2 s 1080 almonds = 3X1 + 2X2 s 240 Cashews = 1X1 + 2X2 s 160
Problem 3 The Silly Nut Company makes two mixtures of nuts: Mixture A and Mixture B. A pound of Mixture A contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for 4 dollars. A pound of Mixture B contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for 15 dollars. The company has 1080 oz of peanuts, 240 oz of almonds, 160 oz of cashews. How many pounds of each of mixtures A and B should the company make to maximize profit? Variable Peanuts Almonds Cashews Price Mixture A 12 1 4 Mixture B 12 2 2 15 Inventory 1080 240 160 A. Decision variables Mixture A = X1 Мixture B - X2 B. Objective Function Maximize (z) = 4X1 + 15X2 C. Constraints peanuts = 12X1 + 12X2 s 1080 almonds = 3X1 + 2X2 s 240 Cashews = 1X1 + 2X2 s 160
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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Solve the optimization problem using linear programming. Find the optimal solution with graph.
Transcribed Image Text:Problem 3
The Silly Nut Company makes two mixtures of nuts: Mixture A and Mixture B. A
pound of Mixture A contains 12 oz of peanuts, 3 oz of almonds and 1 oz of
cashews and sells for 4 dollars. A pound of Mixture B contains 12 oz of peanuts,
2 oz of almonds and 2 oz of cashews and sells for 15 dollars. The company has
1080 oz of peanuts, 240 oz of almonds, 160 oz of cashews. How many pounds
of each of mixtures A and B should the company make to maximize profit?
Variable
Peanuts
Almonds
Cashews
Price
Mixture A
12
3
1
4
Mixture B
12
2
2
15
Inventory
1080
240
160
A. Decision variables
Mixture A = X1
Mixture B = X2
B. Objective Function
Maximize (z) = 4X1 + 15X2
C. Constraints
peanuts = 12X1 + 12X2 < 1080
almonds = 3X1 + 2X2 s 240
Cashews = 1X1 + 2X2 < 160
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