3.4-14. The Metalco Company desires to blend a new alloy of 40percent tin, 35 percent zinc, and 25 percent lead from several avail-able alloys having the following properties:AlloyProperty12345Percentage of tinPercentage of zincPercentage of lead602545205010154550403060103010Cost ($/lb)7770888494The objective is to determine the proportions of these alloys thatshould be blended to produce the new alloy at a minimum cost.(a) Formulate a linear programming model for this problem.c (b) Solve this model by the simplex method.

Let us assume that x1 as the Portion of Alloy 1, whereas x2 for Portion of Alloy 2. Likewise x3, x4…

Answered: (a) Formulate a linear programming…

Practical Management Science

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a. Identify the feasible solution. b. Obtain the optimal solution. Note: Assumer or determine the objective function from available data.
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
Why are constraints in nonlinear programming unnecessary?
A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers, and requires two tons of fertilizer. Each acre plantedwith corn yields $3000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available.a. Use Solver to help the farmer maximize the profit from his land.b. Confirm graphically that the solution from part a maximizes the farmer’s profit from his land.c. Use SolverTable to see what happens to the decision variables and the total profit when the availability of fertilizer varies from 200 tons to 2200 tons in 100-ton increments. When does the farmer discontinue producing wheat? When doeshe discontinue producing corn? How does the profit change for each 100-ton increment?
Discuss several advantages of linear programming; clearly explain the reasons for your choices.

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(a) Formulate a linear programming model for this problem. c (b) Solve this model by the simplex method.