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:

$mamizeZ=50x_1+58x_2+46x_3+62x_4$

subject $to$

$4x_1+3\mathrm{.}5x_2+4\mathrm{.}6x_3+3\mathrm{.}9x_{4}600hr.(process1)$

$2\mathrm{.}1x_1+2\mathrm{.}6x_2+3\mathrm{.}5x_3+1\mathrm{.}9x_{4}500hr.(process2)$

$15x_1+23x_2+18x_3+25x_{4}3,600lb.(materialA)$

$8x_1+12\mathrm{.}6x_2+9\mathrm{.}7x_3+10\mathrm{.}5x_{4}1,700lb.(materialB)$

$\frac{x_1+x_2}{x_1+x_2+x_3+x_4}\mathrm{.}60$

$x_1,x_2,x_3,x_{4}0$

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 product have to be for it to be produced?