A garden store prepares various grades of pine bark for mulch: nuggets $(x_1),$ mini$-$nuggets $(x_2),$ and chips $(x_3).$ The process requires pine bark, machine time, labor time, and storage space. The following model has been developed.

Maximize $9x_1+9x_2+6x_3(profit)$

Subject $to$

Subject to

Bark $,5x_1+6x_2+3x_{3}600$ pounds

Machine $,2x_1+4x_2+5x_{3}600$ minutes

Labor $,2x_1+4x_2+3x_{3}480$ hours

Storage $1x_1+1x_2+1x_{3}150$ bags

$x_1,x_2,x_{3}0$

a$-1.$ What is the marginal value of a pound of pine bark? $($Round your answer to $2$ decimal places.$)$

The marginal value of a pound of bark is

$0-2.$ Over what range is this price value appropriate?

This marginal value is in effect from

Ibs, to

lbs$.$ of bark.

b$.$ What is the maximum price the store would be justified in paying for additional pine bark? $($Round your answer to $2$ decimal ploces.$)$