Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting

$R=$ number $of$ regular gloves

$C=$ number $of$ catcher's mitts

leads to the following formulation:

$]800$ Cutting and sewing $[0,$

The computer solution is shown below.

$\backslash$table$[[$Variable$,$Value,Reduced cost$],[$R$,380\mathrm{.}00000,0\mathrm{.}00000],[$c$,210\mathrm{.}00000,0\mathrm{.}00000],[$Constraint$,\backslash$table$[[$Slack$/$Surplus$],[105\mathrm{.}00000]],$Dual value$],[1,105\mathrm{.}000,0\mathrm{.}00000],[2,\backslash$table$[[0\mathrm{.}0000],[0\mathrm{.}0000]],3\mathrm{.}00000],[3,28\mathrm{.}00000],[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$R$,5\mathrm{.}00000,7\mathrm{.}00000,1\mathrm{.}00000],[$c$,8\mathrm{.}00000,2\mathrm{.}00000,4\mathrm{.}66667],[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,800\mathrm{.}00000.,$Infinite,$105\mathrm{.}00000],[2,260\mathrm{.}00000,140\mathrm{.}00000,126\mathrm{.}66667],[3,100\mathrm{.}00000,21\mathrm{.}00000,35\mathrm{.}00000]]$

$($a$)$ Determine the objective coefficient ranges. $($Round your answers to two decimal places.$)$

regular glove $xto7\mathrm{.}00$

catcher's mitt $to4\mathrm{.}67$

$,$

$($b$)$ Interpret the ranges in part $($a$).($Round your answers to two decimal places.$)$

As long as the profit contribution for the regular glove is between $

and $ $,$ the current solution $-$ Select$-vv$ optimal. As long as the profit contribution for the catcher's mitt is between $ and $ the current solution $-$ Selec optimal.

$($c$)$ Interpret the right$-$hand$-$side ranges.

The dual values for the resources are applicable over the following ranges. $($Round your answers to two decimal places. If there is no upper or lower limit$,$ enter NO LiMI.$)$

cutting and sewing

to

finishing

packaging and shipping

$$ to

$($d$)$ How much will the value of the optimal solution improve $($in $$)$ if $10$ extra hours of packaging and shipping time are made available?