Question

Using the simplex method, find the optimal solution to the following LP: A company manufactures three products, A,B, and C. The sales volume for A is at least 50% of the total sales of all three products. However, the company cannot sell more than 75 units of A per day. The three products use one raw material, of which the maximum daily availability is 240 pounds. The usage rates of the raw material are 2 lb per unit of A, 4 lb per unit of Band 3 lb per unit of C. The unit prices of A,B, and C are $20, $50, and $35 respectively.

Answer 1

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LoM SOX2+ 35m and u2f 3Uzs go 120S(N+) o'sx-oisy-0.52 70 一ローリー20, ne75

= 240 Max Z = 20 X1 + 50 X2 + 35 X3 + 0S1 + 0 S2 + 0 S3 - MA1 subject to 2 X1 + 4 X2 + 3X3 + Si - X - X2 - xz - S2 + A₂ = 0 X1 + S3 = 75 and X1, X2, X3, S1, S2, S3, A1 2 0 Iteration-1 20 50 35 0 0 0 -M в Св | x3 S1 S₂ S3 A1 | MinRatio Хв si 0 240 4 3 1 0 0 0 240 - = 120 0 -1 0 -1 0 1 = = 0 75 Sz 0 75 1 0 0 0 0 0 1 0 * = 75 Z = 0 Z; -M M M 0 M 2;-C; -M -20 M - 50 M-350 M 0 -M 0 0

Iteration-2 50 50 35 0 0 0 MinRatio x x2 x₃ S1 S₂ S3 XB 240 240 -1 = 40 - 6 -1 -1 0 -1 0 75 S3 0 75 0 1 1 0 1 19 = 75 Z = 0 Z; Z;-C; 20 0 -20 -70 1 | -20 | -55 0 -20

Iteration-3 7 = 2800 ه م دادن به این ماده = | د | دن

so we get x1 = 40 , x2=40 and x3=0 ...

maximum sale money = $ 2800