a) Write the optimization problem above as a linear program (b) Argue that the solution occurs at x ∗ = 1/2 (b1 + bm), the midrange of the data points
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A: 18.E.ALL OF THE ABOVE
(a) Write the optimization problem above as a linear program
(b) Argue that the solution occurs at x ∗ = 1/2 (b1 + bm), the midrange of the data points
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- For 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 simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 2x + 9y subject to the following. 2x + 5y ≤ 50 x + 5y ≤ 45 x + y ≤ 14 (x,y)= f=Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 7x + 14y + 4z subject to the following. 3x + 5y + 4z ≤ 30 3x + 2y ≤ 4 x + 2y ≤ 8 (x,y,z)= f=
- A matrix is said to be upper triangular if for i > j, aij=0. Show that the determinant of any upper triangular 3* 3matrix is equal to the product of the matrix’s diagonalelements. (This result is true for any upper triangular matrix.)Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.Consider a school district with I neighborhoods, J schools, and G grades at each school. Each school j has a capacity of C jg for grade g. In each neighborhood i , the student population of grade g is S ig. Finally, the distance of school j from neighborhood i is dij . Formulate a linear programming problem whose objective is to assign all students to schools, while minimizing the total distance traveled by all students. (You may ignore the fact that numbers of students must be integer).
- XYZ Inc. produces two types of paper towels, called regular and super-soaker. Regular uses 2 units of recycled paper per unit of production and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. Letting X1 be the number of units of regular produced per month and X2 represent the number of units of super-soaker produced per month, the appropriate constraint/s will be ___________ a. 2X1 = 3X2 b. 2X1 + 3X2 ≥ 10000 c. 2X1 + 3X2 = 10000. d. 2X1 + 3X2 ≤ 1000Use the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 3x + 22y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 (x,y)= f=Solve using Simplex MethodMaximize z = 4x1 + 3x2subject to-x1 +2x2 ≤43x1 +2x2 ≤14x1 – x2 ≤ 3x1, x2 ≥ 0
- Consider the points (0, 0), (1, 1), and (2, 3). Formulatean NLP whose solution will yield the circle of smallestradius enclosing these three points. Use LINGO to solvethe NLP.Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0