1. Find the solution of the following LP problem using graphical method. Find the integer solution of the same using dual simplex algorithm. Max x1 + x2 Subject to 2x2≤5 X1+x27 2x1≤9 X1, X2 ≥0.

Use the Simplex algorithm to solve the following LP.

Solve the following LP using two-phase simplex algorithm: max z = 3x1 +2x2 st x1 +2x2 >12 x1 +x2 <5 X1,x2 20

Solve the following LP using Big-M simplex algorithm: max z = -3x1 -x2 st x1 +x2 +x3 2 12 4x1 -x2 +x3 26 Xị 2 0 Vi

Consider the system x₁ + x₂ Answer: 3x3 + 4x4 - 4x3 + 5x4 + 2 - 11x3 + 9x4 - 5 5x4 +1 -X1 4x2 + 10x3 Using the GJ algorithm (or otherwise) find the solution (x₁, x2, x3, x4). Write the value of x₂ x1 + x₂ 2x1 + 5x₂ - = 0 = 0 = 0 = 0 =

a. x-1_x²+2x-3 x+2 x+2

Find the number of nonnegative integer solutions to (x₁ + x2 + x3 + x4 + X5) (X6 + X7 + X8 + x9 + X10) = 23.

An article in a sociology journal stated that if a particular health-care program for the elderly were initiated, then t years after its start, n thousand elderly people would receive direct benefits, where =글3-612 + 32t [0, 12] n 3= For what value of t does the maximum number receive benefits? O 12 F9 F8 F7 F5 F6 F4 & 7 96

Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.a. Write down the dual of this LP.b. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.

Simulate the product algorithm for polynomials p and q where p( x ) = 2x³ - 3x² + 9x + 11 and q( x ) = 4x³ - 6x Use a table.