the following linear programming model formulation is used for the production of four different products, with two different manufacturing processes and two different material requirements

maximize Z = 50x₁ + 58x₂ + 46x₃ + 62x₄ subject to

process 1: 4x₁ + 3.5x₂ + 4.6x₃ + 3.9x₄ < 600 hours

process 2: 2.1x₁ + 2.6x₂ + 3.5x₃ + 1.9x₄ < 500 hours

material a: 15x₁ +23x₂ + 18x₃ + 25x₄ < 3600 pounds

material b: 8x₁ + 12.6x₂ + 9.7x₃ + 10.5x₄ < 1700 pounds

(x₁ + x₂) / (x₁ + x₂ + x₃ + x₄) > 0.60

x₁ , x₂, x₃, x₄, > 0

solve a-d

a. solve this problem by using the computer

b. identify the sensitivity ranges for the objective function coefficients and the constraint quantity values

c. which is the most valuable resource to the firm?

d. one of the four products is not produced in the optimal solution.how much would the profit for this have to be for it to be produced?

thank you