Question

Problem 4: Sensitivity Analysis (Total 25 points) Consider the following linear program. Solve using the graphical method. A company manufactures two products, A and B. The unit revenues are $5 and $8, respectively. Two raw materials, M1 and M2 are used. The supply of M1 and M2 are 4 and 12 units, respectively. Maximize z= 5x1 + 8x2 Subject to M1 2x1 + x2 <4 3x1 + 6x2 < 12 X1, x2 > 0 M2 a) Changes in Constraint RHS (13 points) i) Determine the dual prices of M1 and M2 and their feasibility ranges. ii) If 4 additional units of M2 can be acquired at a cost of $0.30 per unit, would you recommend the additional purchase? Page 2 of 3 iii) iv) What is the most the company should pay per unit of M2? If M2 availability is increased by 5 units, determine the associated optimal revenue.

Answer 1

maximize zasu +8X2 subject to 2xy +22 24. 84 +682 512 4, 8270 t 2y+=4 84 +672 =12 Feable -2 -1 0 mery tas 4 braut 622 12 -5 -4 -3 Region OABC is feasible region o coo) (2012) A (2,0) To find coordinates a point B 3 point B is intersection point of lines 2xton = 4 g 334 +682=12 " he solve these eggs of lines 1284 +682 =24 2(3)+12=4 - 324 + 6012 =12 grys 12 24 413 x 4.8/2. [x2=413 ie B (413,413) Now substitute each pogut in objective function. for paint 0(0,0) 2 = 5 (0) 48(0) = 6 for point A (2,0) z = 5(2)48 (0)=10 for point B (413,413) = 5x4/3f 8x4/3 = 20 21 22 = 44 - 14.66 For point c(012) 2 = 5(0)18 (2) = 16 max valve q 2 is 16 which is at (0,2) If company produce units of product is then company will get maximum profit!