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:

Max $5$R $+8$C

s$.$t$.$

R $+$

$3$

$2$

C $<=1,000$ Cutting and sewing

$1$

$2$

R $+$

$1$

$3$

C $<=260$ Finishing

$1$

$8$

R $+$

$1$

$4$

C $<=100$ Packaging and shipping

R$,$ C $>=0$

The computer solution is shown below.

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

Variable Value Reduced Cost

R $380\mathrm{.}000000\mathrm{.}00000$

C $210\mathrm{.}000000\mathrm{.}00000$

Constraint Slack$/$Surplus Dual Value

$1305\mathrm{.}000000\mathrm{.}00000$

$20\mathrm{.}000003\mathrm{.}00000$

$30\mathrm{.}0000028\mathrm{.}00000$

Variable Objective

Coefficient Allowable

Increase Allowable

Decrease

R $5\mathrm{.}000007\mathrm{.}000001\mathrm{.}00000$

C $8\mathrm{.}000002\mathrm{.}000004\mathrm{.}66667$

Constraint RHS

Value Allowable

Increase Allowable

Decrease

$11000\mathrm{.}00000$ Infinite $305\mathrm{.}00000$

$2260\mathrm{.}00000140\mathrm{.}00000126\mathrm{.}66667$

$3100\mathrm{.}0000061\mathrm{.}0000035\mathrm{.}00000$

$($a$)$

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

regular glove to

catcher's mitt 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's mitt is between $ and $ $,$ the current solution 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 $30$ extra hours of packaging and shipping time are made available?

$