Flo uses an alternative method of gardening. Flo has found that happy plants only need fertilizer and talk. Where f is the number of bags of fertilizer used and t is the number of hours she talks to her plants, the number of happy plants produced is exactly h $=$ t $+2$f $($i$.$e$.,$ talk being a perfect substitute for fertilizer$).$ Suppose fertilizer costs wf per bag and talk costs wt per hour.

$($a$)$ If Flo uses no fertilizer, how many hours of talk must she devote if she wants one happy plant? If she doesn$$t talk to her plants at all, how many bags of fertilizer will she need for one happy plant?

$($b$)$ If wt$/$wf $<1/2,$ would it be cheaper for Flo to use fertilizer or talk to raise one happy plant?

$($c$)$ Write down Flo$$s cost function. $1$