Question

1.4 Given the constraints (10) A+B + C <= 24, B +C >=8 and A >= 0, B >= 0, C>=  0. Maximize 24-A-B - C A: amount of time spent on school work B: amount of time spent on fun C: amount of time spent on pay work

Answer 1

Maximize $Z=24-A-B-C$

subject to,

$A+B+C \le 24\\ B+C\ge8\\ A,B,C\ge0$

for simplex calculation,

Maximize $Z=24-A-B-C+0S_1+0S_2-MA_1$

subject to,

$A+B+C+S_1 = 24\\ B+C-S_2+A_1=8\\ A,B,C,S_1,S_2,A_1\ge0$

iteration 1

iteration 2

answer is ,

$\bold{A=0,B=8,C=0}\\ Z_{max}=24-0-8-0=16\\ \bold{Z_{max}=16}$

$\bold{}$