Question

Given the constraints
A+B+C<or=24,B+C>or=8and A>or=0,C>or=0.
Maximize24-A-B

A:amount of time spent on schoolwork
B:amount of time spent on fun
C: amount of time spent on pay work

Answer 1

here in the question only A and C are give as $A,C\ge0$ . But the B is amount of time spent on fun and time also cannot be negative and it should be $B\ge 0.$

This problem is converted to solve using simplex(Big-M) method and it is follows.

$maximize \ 24-A-B+0S_1+0S_2-Ma$

$subject\ to,\\ A+B+C+S_1\hspace{4 em}=24\\ B+C\hspace{4 em}-S_2+a\ =8\\ A,B,C\ge0$

iteration-1

a goes out from the basis and C comes in.

iteration-2

$since\ Z-C_j\ge 0$  optimum solution is occurred.

maximum is occurred when,

A=0,B=0,C=8 and Maximum is 24