$($Easy$-$Carry Suitcase$)$ Easy$-$Carry Suitcase Company $($ECSC$)$ makes three styles of suitcase: $(1)$ Standard, $(2)$

Deluxe, and $(3)$ Luxury. Each suitcase goes through four production stages: $(1)$ cutting and colouring, $(2)$ assembly,

$(3)$ finishing, and $(4)$ quality & packaging. The total number of hours available in each of these departments is $630,$

$600,708,$ and $135,$ respectively.

Each standard suitcase requires $0\mathrm{.}7$ hours of cutting and colouring, $0\mathrm{.}5$ hours of assembly, $1$ hour of finishing, and

$0\mathrm{.}1$ hours of quality & packaging. The corresponding numbers for each Deluxe suitcase are $1$ hour, $0\mathrm{.}83$ hours, $0\mathrm{.}67$

MGSC $1205$

Introduction to Quantitative Methods I

hours, and $0\mathrm{.}25$ hours, respectively. Likewise, the corresponding numbers for each Luxury suitcase are $1$ hour, $0\mathrm{.}67$

hours, $0\mathrm{.}9$ hours, and $0\mathrm{.}4$ hours, respectively.

The sell price for each type of suitcase is as follows: Standard $$39\mathrm{.}95,$ Deluxe $$44\mathrm{.}95,$ Luxury $$54\mathrm{.}95.$ The materials

costs are Standard $$6\mathrm{.}50,$ Deluxe $$8\mathrm{.}50,$ Luxury $$10\mathrm{.}50.$ The hourly cost of labour is $$12$ for cutting and colouring,

$$8$ for assembly, $$10$ for finishing and $$9$ for quality & packaging.

ECSC needs to know how many suitcases of each style should be made in order to maximize the total profit.

a$)$ Formulate the problem as an LP problem.

b$)$ Set this model in Excel. Solve the LP problem using Solver. Attach the Excel output with the LP model,

answer report and sensitive report on one page.

c$)$ According to your optimal solution, how many suitcases of each style should be made in$?$ What is the

maximum total profit?