Question

Question 1 Afariwa farm operates a large farm on which cow are raised. The farm manager Kofi Manu determined that for the cow to grow in the desired fashion, they need at least minimum amounts of four nutrients. Kofi Manu is considering three different grains to feed the cow. The table below lists the number of units of each nutrient in each kilogram of grain, the minimum daily requirements of each nutrient for each cow, and the cost of each grain. The manager believes that as long as a cow receives the minimum daily amount of each nutrient, it will be healthy and produce a standard amount of meat. The manager wants to raise the cow at minimum cost. Grain 1 Grain 2 Grain 3 Minimum daily requirement (units) Nutrient A 20 30 70 110 Nutrient B 10 10 0 18 Nutrient C 50 30 0 90 Nutrient D 6 2.5 10 14 Cost (GH¢) 41 36 96 a) Formulate a linear programming model for this problem. b) Use solver to find optimal solution and sensitivity report. c) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. (d) Advice the management about objective function value corresponding to your answer in (b).

Answer 1

(a)

(b)

Optimal solution :

  

Respective Sensitivity report :

(c)

So to find the optimum quantity, we need to maximize the four nutrients required by cows per unit at the possible minumum cost. Using the Excel Solver, the optimal unit of the required feed was obtained as Grain1 being 0.60/kg, Grain2 being 2.01/kg, and Grain3 being 0.54/kg,

Also as per the sensitivity report, since Nutrient B has a shadow price of 0, it is a non-binding constraint and hence can be ignored in all further analysis

(d)

Depending on the result of optimal solution, the farm manager should procure the three different types of grain in the obtained proportions obtained on a per day basis with daily cost of $149