Question

2. A company produces two types of tables, T1 and T2. It takes 2 hours to
produce the parts of one unit of T1, 1 hour to assemble and 2 hours to
polish.It takes 4 hours to produce the parts of one unit of T2, 2.5 hour to
assemble and 1.5 hours to polish. Per month, 7000 hours are available for
producing the parts, 4000 hours for assembling the parts and 5500 hours for
polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the
total monthly profit?

Answer 1

let units of table T₁ as x and table T₂ as y.

Objective maximize 90x+110y

constraints are,

$2x+4y\le 7000\\ x+2.5y \le 4000\\ 2x+1.5y\le5500$

therefore the optimization problem is,

$$maximize \quad 90x+110y$$

$subject \ to,\\ 2x+4y\le 7000\\ x+2.5y \le 4000\\ 2x+1.5y\le5500$

to evaluate using simplex method,

$maximize \quad 90x+110y+0s_1+0s_2+0s_3$

subject to,

$2x+4y+s_1= 7000\\ x+2.5y+s_2 =4000\\ 2x+1.5y+s_3=5500$

s₂ goes out and y comes to basis

s₁ goes out and x comes to basis

s₃ goes out and s₂ comes to basis

Answer is maximum profit $273000 by making type T₁ table 2300 and type T₂ table 600