Q4. Solve the following Linear Programing problem by using two different methods. (Graphical and Big M methods) Maximize z = 3x1-x2 Subject to constraints: 2x1 + x2 ≤2 x1+3x2 ≥3 X2 ≤4 X1, X20

Let x represent the number of gasoline engines produced and let y represent the number of diesel engines produced.  Write the equation that best describes the objective function   Show your work

You are given the ILP model below: Мaximize Z = -3x1 + 5x2, subject to 5x1 – 7x2 > 3 and X; < 3 X; 2 0 X; is integer, for j = 1, 2. Convert the ILP model above into a BIP model. TIP: You will need to perform the necessary analysis on the constraints to determine the maximum value, u.

Write the dual of the following LPP Minimise Z = 16x₁ + 9x₂ + 21x₃ Subject to the constraints: x₁ + x₂ + x₃ = 16 2x₁ + x₂ + x₃ ≥ 12 x₁ , x₂ ≥ 0 x₃ - unrestricted.

Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.

Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.

A school wants to minimize the transportation cost of taking students on a tield trip. The following polygon of constraints represents the solutions for this situation. 10 8. 7. 3. 5678 9 10 Number of Regular School Buses X: number of regular school buses y. number of minibuses It costs $100 to rent each regular school bus, while each minibus costs $75. Unfortunately, because of mechanical problems, no more than 4 regular school buses are available on the day of the field trip. Because of this, the minimum transportation cost of the field trip will increase. A) By how much will the minimum transportation cost increase? B) How many possible solutions are there in the new solution set? Number of Minibuses

please answer this question in 20 minutes.

(b) maximize ᏆᎪ subject to x4x12x2+4x3, x42x13x2 - 5x3, x43x14x2+6x3, x1 + x2 x3 = 1, x1, x2, x30, x4 unrestricted Hint: Remember to first rewrite all the constraints so that all variables are on the left and the right-hand side is a constant.

Is this constraint linear or able to be included as a constraint in a linear programming problem? 4X1 – (1/3)X2 = 75