Modeling Examiples

Question $1$: The Whitt Window Company, a company with only three employees, makes two different kinds of hand$-$crafted windows: a wood$-$framed and an aluminum$-$framed window. The company earns $$300$ profit for each wood$-$framed window and $$150$ profit for each aluminumframed window. Doug makes the wood frames and can make $6$ per day. Linda makes the aluminum frames and can make $4$ per day. Bob forms and cuts the glass and can make $48$ square feet of glass per day. Each wood$-$framed window uses $6$ square feet of glass and each aluminumframed window uses $8$ square feet of glass. The company wishes to determine how many windows of each type to produce per day to maximize total profit.

Solution:

$x_1$: wood $-$ framed

$x_2$ : aluminum $-$ framed

Max,$z=300x_1+150x_2$

$s.t.6x_1+8x_{2}48$

$,0x_{1}6$

$,0x_{2}4$