Write the linear programming model for this problem and use Excel to solve it$.$ Save the sensitivity analysis and

a$.$ What is the optimum solution, and what is the value of the objective function?

b$.$ Which constraints are binding, and which have excess capacity?

c$.$ Explain the meaning of all the values under the Reduced Cost column. Be very specific.

d$.$ If the objective function coefficient of a desk $($profit per unit$)$ is increased by $$3\mathrm{.}50,$ will the optimal solution Change? Fully explain.

e$.$ Suppose the profit per unit for tables is increased by $$1,$ for chairs is decreased by $$2,$ and for bookshelves is Would the optimum solution change? What will be the new value of the objective function? $($Range of Optin

f$.$ Identify the range of feasibility for the right$-$hand$-$side values and fully explain their meanings.

g$.$ Fully interpret the meaning of the Shadow Prices $($Dual Prices$).$

h$.$ A painter has offered his services for painting on this project at a price below the minimum wage. Should we obtain the hours? Why or why not? Fully explain.

i$.$ If you could get additional time in all three departments, which department should get priority and why?

j$.$ Twenty hours of finishing time can be purchased at $25$ cents per minute above the current cost. Should we obtain the additional hours? If yes, what will be our total profit after paying for the time used.

k$.$ Refer to part $"$a$"$ of this problem. One of the company's best clients has requested $10$ chairs. If the company decides to produce the requested units of chairs, what would be the new total profit?