A firm uses a turning center, a milling center and a grinding

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A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts I and II are Rs. 40 and Rs. 100, respectively. The maximum profit per week of the firm is Rs. ________

1. 40,000
2. 40,00
3. 30,000
4. 20,000

Correct Option: A

Zmax =40x + 100y
S.t 12x + 6y ≤ 6000, 4x + 10y ≤ 4000
2x + 3y ≤ 1800 x, y ≥ 0

	x	+	y	≤ 1	x	+	y	≤ 1
	500		1000		1000		400

	x	+	y	≤ 1
	900		600

12x + 6y = 6000
4x + 10y = 4000

	12x + 6y = 6000 12x + 30y = 12000
	- 24y = - 6000

y =	6000	= 250
	24

4x + 10y = 4000
4x + 250 × 10 = 4000
4x = 1500

x =	1500	= 375
	4

Z_max =40x + 100y
= 40 × 375 + 100 × 250
= 15000 + 25000
Z_D = 40,000/-
Z_A = 0
Z_B = 40 × 500 + 100 × 0
= 20,000
Z_C = 40 × 0 + 100 × 400
= 40,000
Optional at (D) & (C).