You are preparing a diet of meat and spinach which must provide at least 1200 mg

Question

You are preparing a diet of meat and spinach which must provide at least 1200 mg of protein and at least 1000 mg of iron. Each pound of meat contains 500 mg of protein and 100 mg of iron. Each pound of spinach contains 200 mg of protein and 800 mg of iron. If meat cost $3.00 per pound and spinach cost $1.50 per pound, what s the minimum cost such a diet can have? You do not have to solve this problem, just write out the model and the initial tableau as requested below. (a) Write a mathematical model for this problem; (i) choose appropriate variables and say what they represent, (ii) give the objective faction and say whether it is to be maximized or minimized; (iii) write oat the constraints. (b) Write the initial tableau for solving this problem by the simplex method.

Explanation / Answer

Minimum Protein = 1200 mg; Minimum Iron = 1000 mg

Each pound of meat contains 500mg of Protein and 100 mg of Iron

Each pound of Spinach contains 200mg of Protein and 800mg of Iron

Meat = $3 per pound and Spinach = $1.5 per pound

a) Decision variables here would be the amount in pound of Meat and Spinach that should be used to minimize the cost wihile keeping constraints in mind.

Let amount of Meat be m and amount of Spinach be s

Objective function:

Min Z = 3m + 1.5s

Constraints:

500m + 200s 1200 (Protein should me minimum of 1200mg)

100m + 800s 1000 (Iron should me minimum of 1000mg)

m 0, s 0

b) We will add slack variables for both the constraints x1, x2

500m + 200s - x1 = 1200

100m + 800s - x2 = 1000

Z = 3m + 1.5s => -3m - 1.5s + Z = 0

m s x1 x2 Z RHS 500 200 -1 0 0 1200 100 800 0 -1 0 100 -3 -1.5 0 0 1 0

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