Hot&Cold and CaldoFreddo are two European manufacturers of homeappliances that have merged. Hot&Cold has plants in France, Germany, and Finland, whereas CaldoFreddo has plants in the UnitedKingdom and Italy. The European market is divided into four regions: north, east, west, and south. Plant capacities $($millions of units per year$),$ annual fixed costs $($millions of euros per year$),$ regional demand $($millions of units$),$ and variable production and shipping costs $($euros per unit$)$ are as shown in

Table $5-13$ Capacity, Cost, and Demand Data for Hot&Cold

and CaldoFreddo. Each appliance sells for an average price of $300$ euros. All plants are currently treated as profit centers, and the company pays taxes separately for each plant. Tax rates in the various countries are as follows: France, $0\mathrm{.}25$; Germany, $0\mathrm{.}25$; Finland, $0\mathrm{.}3$; UK$,0\mathrm{.}2$; and Italy,$0\mathrm{.}35.$

For each case below, provide i$)$ Integer programming formulation ii$)$ optimizer software output $($Formulation and solution$),$ and iii$)$ Network design in tabular format.

a$.$ The case before the merger where all plants are kept open if the objective is cost minimization $($Production and shipping costs as well as annual fixed cost$)$

b$.$ The case before the merger where all plants are kept open if the objective is after$-$tax profit maximization.

c$.$ In the case after the merger where all plants are kept open if the objective is cost minimization $($Production and shipping costs as well as annual fixed costs$)$

d$.$ In the case after the merger, where all plants are kept open if the objective is after$-$tax profit maximization.

e$.$ The case after the merger if the plants can be shut down $($Saving annual fixed cost for the shutdown plant$($s$)$ if the objective is cost minimization.

f$.$ The case after the merger if the plants can be shut down $($Saving annual fixed cost for the shutdown plant$($s$)$ if the objective is after$-$tax profit maximization.