Question

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

Answer 1

Correct option is (C)

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.

`(30)/(60)t+(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`