Question

Help please inequalities are kicking my butt any help is greatly appreciated thank you in advance

Answer 1

Answer:

Correct option is (C)

Step-by-step explanation:

we are given that -Tim design a pair of shorts,S, and T-shirts,t.

Tim sell Sorts for $12 and T-shirts for $8 each.

Tim can work atmost 18 hours a day so we can write $time\leq 18$

Time taken to design a T-shirt is 30 minutes and for Shorts, it is 45 minutes.

$\frac{30}{60}t+\frac{45}{60}s\leq 18\\\text{Multiply both the sides by 60}\\30t+45s\leq 1080\\\text{Divide both the sides by 45}\\s+0.66t\leq 24\\\text{Subtract 0.66t from both the sides}\\s\leq 24-0.66t$

He must design 12 itesm each day, so we can write $t+s\geq 12$

Further it can be written as

$t+s\geq 12\\\text{Subtract t from both the sides}\\s\geq 12-t$

Also Tim can not design more than 30 items in one day, so we can write

$t+s\leq 30\\\text{Subtsract t from both the sides}\\s\leq 30-t$

Hence from the above equations , its claer that

$s\geq 12-t,s\leq 30-t,s\leq 24-0.66t,s\geq 0,t\geq 0$