NAME: 2 MT263 problems Hand in your solutions, with this coversheet, for feedback at the start of the MT263 lecture on Wednesday 16th October. Late submissions should be handed into the School office in the Bedford building. I will keep a record of how many questions you made a decent attempt on. I can provide you with additional feedback if you want it. Many students don't collect their feedback so if you don't want additional feedback, please tick the relevant box below. Otherwise, if you make a decent attempt of N questions, you can request additional feedback on [+] questions (note the use of the floor function here). Please indicate which questions you'd like feedback on in the relevant box below (if you don't indicate what feedback you want, I'll assume you don't want any). • Put a tick in this box if you don't want additional written feedback on your solutions. · I attempted questions. Please provide me with feedback on questions YOUR FEEDBACK TO THE LECTURER (e.g., what was hard, interesting, fun, etc. this week): FEEDBACK ON YOUR SOLUTIONS FROM THE MARKER: 1. Construct initial feasible dictionary for maximise 5x1+ 5x2 subject to 2. Is 1 ? 0 -2x1+ 3x2 ? 2 4x1- 22 > 0. x1, x2 x3 = 2x1 ?1 + x2 + 2x2 x4 = 2 = + 2x2
a feasible dictionary for maximise subject to x1+ 2x2 2x1 + 4x2 ? 1 ? x1 + @2 <- 2 x1, X2 ?0 3. Write down the LPP problem and the solution corresponding to the dictionary x3 = 2 + x1 + 3x2 = 4 - X1 + x2 z = x1 + 2x2 4. Each of the following dictionaries appears as a step in the simplex method for some LPP. For each dictionary, complete the next step of the simplex method (i.e., do one pivot, or if the dictionary is final solve the LPP.) (a) ?3 = 2 + x1 + 3x2 ?4 = 4 - + x2 z = - x1 + 2x2 (b) ?4 x3 x6 z = 1 = 3 = 2 2x5 - 2x1 + 4x2 6x5 + - - 3x2 4x5 = -13 x2 8x5 (c) ?4 = 1 2x3 = 3 - 2x1 + 4x2 6x3 x6 = 2 + x1 z = - 3x2 2x1 - x2 4x3 + 8x3 5. Solve the following LPP using the simplex method. maximise 2x1+3x2 + 2x3 <60 3x1 + 2x2 <10 -x1+ @2 + 4x3 2x1- 2x2 + 5x3 < 50 x1, 12, 13 > 0 For checking your computations, you should get z = 70. 6. Solve the following LPP using the simplex method. maximise subject to 3x1+ 2+ 2x3 x1+x2+3x3 ?30 < 24 2x1+ 2x2 + 5x3 4x1+ x2 + 2x3 ? 36 ?0. x1, I2, I3 For checking your computations, you should get z = 28. 7. Write a flow chart that describes how to apply the simplex method if you are given an initial feasible dictionary. Include