Problem 2: A diet to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of vitamins, 30 units of minerals and 10 calories. Each unit of Food B provides 20 units of vitamins, 20 units of minerals , and 40 calories. Food A costs 2 dollars per unit and Food B cost 1 dollars per unit. How many units of each food should be purchased to keep costs at a minimum? DATA SUMMARY CHART Variable Vitamins Minerals Cost Food A 50 30 2
Problem 2: A diet to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of vitamins, 30 units of minerals and 10 calories. Each unit of Food B provides 20 units of vitamins, 20 units of minerals , and 40 calories. Food A costs 2 dollars per unit and Food B cost 1 dollars per unit. How many units of each food should be purchased to keep costs at a minimum? DATA SUMMARY CHART Variable Vitamins Minerals Cost Food A 50 30 2
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 2:
A diet to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200
calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A
provides 50 units of vitamins, 30 units of minerals and 10 calories. Each unit of
Food B provides 20 units of vitamins, 20 units of minerals , and 40 calories. Food
A costs 2 dollars per unit and Food B cost 1 dollars per unit. How many units of
each food should be purchased to keep costs at a minimum?
DATA SUMMARY CHART
Variable
Vitamins
Minerals
Cost
Food A
50
30
Food B
20
20
1
A diet contain:
2400
1800
A. Decision variables
Food A = X1
Food B = X2
B. Objective Function
Minimize (z) = 2X1 + 1X2
C. Constraints
vitamins = 50X1 + 20X2 s 2400
minerals = 30X1 + 20X2 s 1800
calories = 10X1 + 40X2 < 1200
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