QUESTION 2: LINEAR PROGRAMMING 30 MARKS

Pernel Witter has modernised his farm and is exploring all areas to cut cost. One of his major cost 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. Pernel 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.

Pernel 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.	90 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 X₁ and X₂ 2 marks

b) Derive Pernel's objective function in terms of X₁ and X₂ 3 marks

c) What are the constraints under which Pernel has to operate 7 marks

d) Graphically illustrate the Feasible Region 7 marks

e) Label the corner points using coordinates e.g B(2,6) 6 marks

f) What is the combination that optimises the objective function 3 marks

g) Determine what it will cost Pernel based on his objective 2 marks

NB. Please show working