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 24-A-B - C

given the constraints A+B + C $\leq$ 24, B +C $\geq8$ and $A\geq0, B\geq0, C\geq0$

Then

$$8\leq A+B+C\leq24$$

$$0\leq 24-A-B-C\leq16$$

$24-A-B-C$ has maximum value of 16 when

$$A=0, B+C=8, B\geq0, C\geq0$$