Consider the following all-integer linear program. 1x₁ + 1x₂ Max s.t. 5X1 + 6x₂ 31 1x₁ + 5x₂ ≤ 20 2x₁ + 1x₂ ≤ 11 X₁, X₂20 and integer (a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. X2 X2
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- Use the simplex method to find the optimal solution. Assume all variables are nonnegative. Minimize f = 7x + 9y subject to the following constraints. x2 5 y ≤ 19 -x + y 2 2 X = y = f= Need Help? Submit Answer xxx Read ItFor the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3DUse the graphical 2-D method to maximize subject to If there are no solutions, enter None for z. Maximum value is z = where x1 = and x2 = x1 3x1 X1 z = 6x1 + 2x2 + X2 + 4x2 + 3x2 X1 ≥ 0 > 21 72 <44 X2 ≥ 0
- 2(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a non-basic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering non basic variable. Basic x1 X2 X3 X4 X5 X6 X7 X8 solution -5 4 -1 -10 620 X8 3 -2 -3 -1 1 12 X3 1 1 3 1 3 X1 1 -1 -4 (i)Categorize the variables as basic and non-basic and provide the current values of all the variables. (ii)Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of Z. If each such 3 variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in Z. (iii)Repeat part (b) assuming that the problem is of the minimization type. (iv)Which non basic variable(s) will not cause a change in the value of Z when selected to enter the solution? (b) Let xij be the amount shipped from source i to destination j in a 5X5…Your Manufacturing company has been tasked with building Televisions, computers, and microwaves. To make these products, there are three sub components: Capacitors, Resistors, and Processors. Below shows the maximum number of Televisions, computers, and microwaves we can make along with the maximum number of capacitors, resistors, and processors available to make them. Your Revenue function is determined as $2 for every capacitor used, $3 for every resistor, and $25 for each processor. However, there are FIXED costs if you decide to use the these. If you use Capacitors, it will have a fixed cost of $50, Resistors will have a fixed cost of $60, and Processors have a fixed cost of $250. The total profit is Revenue - Cost. Objective: Determine how many Capacitors, resisters, and processors to use in order to maximize profit. You will also need to capture if you choose to use Capacitors (SC), Resistors (SR), and Processors (SP). (NOTE: The profit is made up of 6 numbers: First three for…Minimize Z= x1+2x2-3x3-2x4 subject to: x1+2x2-3x3+x4=4 x1+2x2+x3+2x4=4 x1, x2, x3,x4 are equal or greater then zero
- Which of the following is the optimal value of the objective function for the LP model in this problem? Minimize z=4x + 8y Subject to: x+1.6y>=45 2x+0.5y>=40 X+y<=40 XY>=0 a.220 b.160 c.240 d.200Simplex Method Write in normal form and solve by the simplex method, assuming x, to be nonnegative. 1. The owner of a shop producing automobile trailers wishes to determine the best mix for his three products: flat-bed trailers, economy trailers, and luxury trailers. His shop is limited to working 24 days/month on metal- working and 60 days/month on woodworking for these products. The following table indicates production data for the trailers. Usage per unit of trailer Flat-bed Economy Luxury Available resources 1 2 1 24 Metal work days Wood work days Contribution (Rx100) 60 4 6 2 14 13Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.
- 3. SOLVE USING TWO-PHASE METHOD Minimize x₁ - 3x3 subject to x₁ + 2x₂x3 ≤ 6 - x₁ - x₂ + 3x3 = X1, X2, X3 20For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.Aa6. please solve with formulas not excell