Solve the following LPP using the simplex method:

SECTION C: Answer four questions. Each question carries ten marks $[4\backslash$times $10=40].$

A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires $3$ hours of assembly, $2$ hours of finishing, and $1$ hour of inspection. Each chair requires $2$ hours of assembly, $2$ hours of finishing, and $1$ hour of inspection. The selling price per table is $$120$ while the selling price per chair is $$80.$ Currently, each week there are $200$ hours of assembly time available, $180$ hours of finishing time, and $40$ hours of inspection time. Assume that one hour of assembly time costs $$4\mathrm{.}00$; one hour of finishing time costs $$5\mathrm{.}00$; one hour of inspection time costs $$3\mathrm{.}50$; and that whatever labor hours are not required for the table and chairs can be applied to another product. Formulate as a Linear programming problem, and develop the optimal production schedule.

Solve the following maximisation traveling salesman problem using the Hungarian assignment method $($note that some of the assignments are restricted$)$:

$\backslash$table$[[,$A$,$B$,$C$,$D$,$E$],[$A$,-,38,41,-,39],[$B$,32,-,34,46,35],[$C$,36,32,-,35,-],[$D$,41,37,-,-,43],[$E$,34,40,32,38,-],[,,,,,]]$

Solve the following LPP using the two$-$phase method:

minw$=2x_1+3x_2$

$st.x_1+x_{2}100$

$2x_1+x_{2}10$

$3x_1+x_2=60$

$x_1,x_{2}0$

maxz$=x_1+2x_2$

$st.2x_1-3x_{2}120$

$-x_1+2x_{2}80$

$3x_1+4x_{2}180$

$x_1,x_{2}0$

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