P Q R S A biologist has 500 kg of nutrient A, 800 kg of nutrient B, and 200 kg o

Question

P Q R S A biologist has 500 kg of nutrient A, 800 kg of nutrient B, and 200 kg of nutrient C. These nutrients will be used to A 0 0 37.5 37.5 B o 20 25 62.5 make 4 types of food, whose contents (in percent per kilogram of food) and whose "growth values' are shown on C 100 80 37.5 0 the right. Set up the initial simplex tableau that would be Growth 100 80 70 60 used to determine how many kilograms of each food Value should be produced in order to maximize total growth Let x1 be the number of kilograms of food type P. Letx2 be the number of kilograms of Q. Let x3 be the number of kilograms of R, and let x4 be the number of kilograms of S. What is the objective function? X1 X2 X2 X Set up the initial simplex tableau for the problem 0 0 1 0 0 500 0.2 0.25 0.625 0 1 0 1 0.8 0.375 0 0 0 1 L 70 60 0 0 0 0 (Type an integer or decimal for each mat

Explanation / Answer

The objective value function is given by :

z = 100 x1 + 80 x2 + 70 x3 + 60 x4

The equations are given by :

0x1 + 0x2 + 0.375 x3 + 0.375x4 + s1= 500

0x1 + 0.20x2 + 0.25x3 + 0.625x4 + s2= 800

1x1 + 0.80x2 + 0.375x3 + 0x4 + s3= 200

Here s1, s2, s3 are slack variables in order to balance these equations

The initial simplex table is therefore given by considering the coefficients of the variables in each row of these equations and it is as follows:

x1 x2 x3 x4 s1 s2 s3 0 0 0.375 0.375 1 0 0 500 0 0.2 0.25 0.625 0 1 0 800 1 0.8 0.375 0 0 0 1 200 -100 -80 -70 -60 0 0 0 0

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