QUESTION 1: LINEAR PROGRAMMING 25 MARKS Greg Samuels a recent UTech graduate has inherited a chicken farm business from his father. He has modernised the farm and is exploring all areas to cut cost. One of his major costs is that of chicken feed. He has just acquired a lucrative contract from Best Dress Chicken, which states some minimum standard for chicken feed which must be maintained. Greg currently buys two brands of feed from Nutramix, Plump Growth and Real Growth. A pound of Plumb Growth cost $.02 and a pound of real Growth cost $0.03. Greg would like to determine the lowest cost diet that meets the minimum monthly feeding requirement per chicken. The table below contains relevant information about the composition of Plump Growth and Real Growth, as well as the minimum monthly requirement for each nutritional ingredient for chicken as stipulated Best Dress Chicken. Composition of Each Pound of Feed INGREDIENT

PLUMP GROWTH

REAL GROWTH

MINIMUM MONTHLY REQUIREMENT

A. 5 oz. 10 oz. 9 0 oz.

B. 4 oz. 3 oz. 48 oz.

C. 0.5 oz. 0 1.5 oz.

D. 0 0.75 oz. 1.5 oz.

a) Express the decision variables in terms of X and Y1 marks b) Derive Gregs objective function in terms of X and Y3 marks c) Construct the constraint equations/inequations under which Greg has to operate5 marks d) Graphically illustrate the Feasible Regionfor Gregs operation.5 marks e) Label the corner points using coordinates e.g., B (2,6)-N.B-This graph has 3 points.6 marks f) Determine the combination that optimises Gregs objective function.4 marks g) State the cost of the monthly feed, based on Gregs objective.1 marks