Question

How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

Answer 1

Amount of	P(x)	Q(y)
Calcium	12	3
Iron	4	20
Chlosterol	6	4
Vitamin A	6	3

Z = 6x + 3y subject to the constraints 

(i) 12x + 3y ≥240 ⇒ 4x + y ≥ 80 

(ii) 4x + 20y ≥ 460 ⇒x + 5y ≥115 

(iii) 6x + 4y ≤ 300 ⇒ 3x + 2y≤150 

(iv) x ≥0 ; y≥0

ABC is the solution region 

A (15,20) Z = 6 x 15+ 3 x 20= 150 

B(40,15) Z = 6 x 40+ 3 x 15 = 285 

C (2,72) Z = 6 x 2 + 3 x 72 = 228

Vitamin A is maximised at B (40,15) to 285 if P contains 40 units and Q containts 15 units.