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.

Optimal Objective Value $=3580\mathrm{.}00000$

$\backslash$table$[[$Variable$,$Value,Reduced Cost$],[$R$,380\mathrm{.}00000,0\mathrm{.}00000],[C,210\mathrm{.}00000,0\mathrm{.}00000],[,,],[$Constraint$,$Slack$/$Surplus$,$Dual Value$],[1,105\mathrm{.}00000,0\mathrm{.}00000],[2,0\mathrm{.}00000,3\mathrm{.}00000],[3,0\mathrm{.}00000,28\mathrm{.}00000]]$

$\backslash$table$[[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$R$,5\mathrm{.}00000,7\mathrm{.}00000,1\mathrm{.}00000],[$C$,8\mathrm{.}00000,2\mathrm{.}00000,4\mathrm{.}66667]]$

$\backslash$table$[[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,800\mathrm{.}00000,$Infinite,$105\mathrm{.}00000],[2,260\mathrm{.}00000,140\mathrm{.}00000,126$

$\backslash$table$[[$R$,5\mathrm{.}00000,7\mathrm{.}00000,1\mathrm{.}00000],[C,8\mathrm{.}00000,2\mathrm{.}00000,4\mathrm{.}66667],[$Constraint$,$RHS$,$Allowable,Allowable$],[1,$Value,Increase,Decrease$],[2,800\mathrm{.}00000,$Infinite,$105\mathrm{.}00000],[3,260\mathrm{.}00000,140\mathrm{.}00000,126\mathrm{.}66667],[,100\mathrm{.}00000,21\mathrm{.}00000,35\mathrm{.}00000]]$

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

regular glove

to

catcher's mitt

$x$ to

$($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 optimal. As long as the profit contribution for the catcher mitt is between $ and $ $,$ the current solution $--$ Select$---vv$ 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 LIMIT.$)$ cutting and sewing to finishing to 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 avale

$$\mathrm{.}66667],[3,100\mathrm{.}00000,21\mathrm{.}00000,35\mathrm{.}00000]]$