Question

Problem A: Consider the following LP problem to answer Questions 4 and 5. Maximise z = 5x1 + 4x2 Subject to 6X1 + 4x2 < 24 X1 + 2x2 5 6 -X1 + x2 <1 X2 < 2 X1, X2 > 0 Question 4 Refer to Problem A: Which of the following statements is correct? (1) The optimal value of x1 is in the interval [10, 15). (2) The optimal valu X2 is in the rval [0, 5). (3) The optimal value of z is in the interval [25, 30). (4) The optimal value of z is in the interval [35, 40). Question 5: Refer to Problem A: Suppose that the second constraint, xy + 2x2 < 6, is eliminated from the above LP problem. Now we consider this modified LP problem. Which of the following statements is correct? (1) The modified LP problem becomes unbounded. (2) The modified LP problem becomes infeasible. (3) The optimal value of xų is in the interval [2, 5]. (4) The optimal value of z is in the interval [17, 20).

Answer 1

Max = 54, +42 Equirlent que sit 6x + 4H₂ 2 24 14 4 t x + 2x, 26 t WF 2 2 2 2 t x2 =2 62,tume=24 1 = ?X+X- 4 M B ne = 2 Jo, +222 = 6 A A010 - E 2 3 $ -1 O ABCDE ú quality After getting fraichle nying fraithe region drawing constraint & get the region of get the peauble rugin. draw the line constant c any 5x + 40 = 20 then that Line the outemost point is waking, to Got met de porte of oy to we with c=20 more point of pa 11 it as

these two 671 +42 = 24 1, +20₂ = 6 w s is intenection lines 64, + 4x = 24 221 + 4 U, =12 42 = 12 3 + 2x₂ = 6 } = 5x3 + 4x 3 3구 87를 = 21 ₂ Elo, s] и ture options 2. remore at its And i And Now from previous fiy if the feaille he name O ABYE caping y" 4. optimal point became 7 shifting I love of objective for OABYE SOARC DE max. (OABYE) 2 in e L2,s] ů the max (OABCDE) anly option lyft option 3 i by solving eque connect for bit da, = 24 2. = 2 x = 16% On TH