Problem $10$: $($Difficulty level: $1)$

In the following example given in the lecture slides in Lecture $1,$ the floor space constraint formula is not reasonable $($why$?).$ Formulate three new LP problems by adding necessary information about the floor space and the dimensions of the machines to model three different floor space constraints. Then solve each of the three problems using both MATLAB Optimisation Toolbox and Excel Solver. After that, fix the number of machine A as $5$ and obtain LP problems with two variables and then solve the two variable LP problems using the simplex method.

MyPC Company invests $$12$ million to buy $3$ models of Component Placement Machines $A,B,C$ to manufacture different kinds of motherboards for personal computers. Total number of operators available is $100.$ A floor space constraint needs to be satisfied. Determine how many of each kind is appropriate to maximise the number of boards manufactured per day.

$\backslash$table$[[\backslash$table$[[$Machine$],[$model$]],\backslash$table$[[$Board$],[$types$]],$Boards$/$hour$,\backslash$table$[[$Operators$],[/$shift$]],\backslash$table$[[$Operable$],[$hours$/$day$]],$Cost$/$machine$],[$A$,10,55,1,18,400,000],[$B$,20,50,2,18,600,000],[$C$,18,50,2,21,700,000]]$