$1.$

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ASWQUANT$138.$E$\mathrm{.}006.$

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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 $<=280$ Finishing

$1$

$8$

R $+$

$1$

$4$

C $<=100$ Packaging and shipping

R$,$ C $>=0$

The sensitivity report is shown below.

Variable Cells

Model Variable Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease

R Gloves Standard $440\mathrm{.}0000\mathrm{.}0005\mathrm{.}0007\mathrm{.}0001\mathrm{.}000$

C Gloves Deluxe $180\mathrm{.}0000\mathrm{.}0008\mathrm{.}0002\mathrm{.}0004\mathrm{.}667$

Constraints

Constraint Number Name Final Value Shadow Price Constraint R$.$H$.$ Side Allowable Increase Allowable Decrease

$1$ Cutting and Dyeing Hours Used $710\mathrm{.}0000\mathrm{.}0001,000\mathrm{.}0001$E$+30290\mathrm{.}000$

$2$ Finishing Hours Used $280\mathrm{.}0003\mathrm{.}000280\mathrm{.}000120\mathrm{.}000146\mathrm{.}667$

$3$ Packaging and Shipping Hours Used $100\mathrm{.}00028\mathrm{.}000100\mathrm{.}00058\mathrm{.}00030\mathrm{.}000$

$($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

$---$Select$---$

optimal. As long as the profit contribution for the catcher's mitt is between $

and $

$,$ the current solution

$---$Select$---$

optimal.

$($c$)$

Interpret the right$-$hand$-$side ranges.

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

cutting and sewing

to

finishing

to

packaging and shipping

to

$($d$)$

How much will the value of the optimal solution improve $($in $$)$ if $50$ extra hours of packaging and shipping time are made available?

$