Q$1.$ The Notip Table Company sells two models of

its patented five$-$leg tables. The basic version uses

a wood top, requires $0\mathrm{.}6$ hour to assemble, and

sells for a profit of $$200.$ The deluxe model takes

$1\mathrm{.}5$ hours to assemble because of its glass top, and

sells for a profit of $$350.$ Over the next week the

company has $300$ legs, $50$ wood tops, $35$ glass tops,

and $63$ hours of assembly available. Notip wishes

to determine a maximum profit production plan

assuming that everything produced can be sold.

Formulate a mathematical programming

model with $4$ main constraints to select

an optimal production plan using de$-$

cision variables $x_1$ number of basic

models produced and $x_2{}_{{?}_{?}}$ number of

deluxe models.