$1$ Graphical and Simplex Method of Linear Programming $-33\mathrm{.}33$ Pts

Many workers. were displaced by the closure of Bamangwato Concessions Ltd$.($BCL$)$ mine in Selebi$-$

Phikwe. Families now have to find new source of income to survive. As heads of families struggle

to find work in nearby villages, a cottage industry is started by a Housewives Cooperative of Selibe

Phikwe $($HCSP$).$ They found a way to make baskets from thorns of bushes that are in abundance almost

everywhere.

A basket maker takes $15$ minutes to pr$$duce a basket. Each basket maker works $150$ hours$/$month$,$

plus up to $40$ hours$/$month overtime. A basket maker is paid a regular saiary of P$2000/$month plus

P$50/$hour for overtime. A basket maker can be hired or fired at the beginning of a month. It costs

P$1500$ to hire a worker and P$1900$ to fire a worker.

The monthly holding cost per basket is $4\%$ of the cost of producing a basket with regular$-$time labor.

$($The raw materials in a pair of shoes cost P$25.)$ At the beginning of month $1,$ the basket makers have

$13$ workers. Formulate the LP that minimizes the cost of meeting on time the demands of the next six

months.

a$.)(10$ points$)$ Setup the above problem as an LP problem.

b$.)(10$ points$)$ Draw the graph of the feasible region of the LP problem.

c$.)(13\mathrm{.}33$ points$)$ Solve the LP problem using Simplex Method and compare the result from the graph$-$

ical method.