Linear Programming Example: Flair Furniture Company

Flair Furniture Company produces inexpensive tables and chairs. The production process

for each is similar in that both require a certain number of labor hours in the carpentry

department and a certain number of labor hours in the painting department. Each table

takes $3$ hours of carpentry work and $2$ hours of painting work. Each chair requires $4$ hours

of carpentry and $1$ hour of painting. During the current month, $2,400$ hours of carpentry

time and $1,000$ hours of painting time are available. The marketing department wants Flair

to make no more than $450$ new chairs this month because there is a sizable existing inven$-$

tory of chairs. However, because the existing inventory of tables is low, the marketing

department wants Flair to make at least $100$ tables this month. Each table sold results in a

profit contribution of $$7,$ and each chair sold yields a profit contribution of $$5.$

Flair Furniture's problem is to determine the best possible combination of tables and

chairs to manufacture this month in order to attain the maximum profit. The firm would

like this product mix situation formulated $($and subsequently solved$)$ as an LP problem. Flair Furniture

$T$ : Number $($amount$)$ of tables to be produced

$C$ : Number $($amount$)$ of chairs to be produced

Maximize profit $=$$$7T+$$$5C$

Subject $to$

$3T+4C2,400(carpentry$ time$)$

$2T+1C1,000(painting$ time$)$

$C450(maximum$ chairs allowed$)$

$T100(minimum$ tables required$)$

$T,C0(nonnegativity)$ Graphical Representation

$**************$How we find the values on Optimal corner point $($ t:$320$ and c:$360)**********$