$($Note: Numerical answers should be either exact orgien

$($Refer to the previous worksheet.$)$

determine how many of type $A(x_A)$ and type $B(x_B)$ cups to produce to maximize the total profit. The LP formulation and the sensitivity report generated by Excel Solver are given on the right.

a$)$ Determine the optimal solution and the maximized total profit.

b$)$ Write the Excel formula set in the cell of the total profit $($suppose that the objective function coefficients, $$50$ and $$60,$ are stored in cells $C3$ and $D3$ respectively$).$

c$)$ Without solving the LP problem again, find the optimal solution and the maximized total profit if both the unit profits of A and $B$ become $$55.$

d$)$ Find the shadow price of the MOQ constraint $($K$).$

e$)$ Without solving the LP problem again, find the maximized total profit if the RHS of the Cutting, Assembly and MOQ constraints become $3$ hours, $x_A+x_{B}10($MOQ$)x_A,x_{B}0$ Cutting$)($Assembly$)$

$\backslash$table$[[,,\backslash$table$[[$Final$],[$Value$]],\backslash$table$[[$Reduced$],[$Cost$]],\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$$$C$$$2,$Type A$,8,0,50,25,12\mathrm{.}5],[$$D$$2,$Type B$,20,0,60,20,20]]$

$\backslash$table$[[$Constraints$,,,,,,],[,,$Final,Shadow,Constraint,Allowable,Allowable$],[$Cell$,$Name,Value,Price,R$.$H$.$ Side,Increase,Decrease$],[$$$E$$$6,$Cutting,$200,5,200,40,80],[$$$E$$$7,$Assembly,$240,2\mathrm{.}5,240,160,40],[$$$E$$$8,$MOQ,$28,K,10,18,1E+30$