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ASWQUANT$138.$E$\mathrm{.}005.$

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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 $5R+7C$

$s.t.$

$,R+\frac{3}{2}C800$ Cutting and sewing

$\frac{1}{2}R+\frac{1}{3}C300$ Finishing

$\frac{1}{8}R+\frac{1}{4}C100$ Packaging and shipping

$R,C0,$

The sensitivity report is shown below.

Variable Cells

$\backslash$table$[[$Model Variable,Name,Final Value,Reduced Cost,Objective Coefficient,Allowable Increase,Allowable Decrease$],[$R$,$Gloves Standard,$500\mathrm{.}000,0\mathrm{.}000,5\mathrm{.}000,5\mathrm{.}500,1\mathrm{.}500],[$C$,$Gloves Deluxe,$150\mathrm{.}000,0\mathrm{.}000,7\mathrm{.}000,3\mathrm{.}000,]]$

Constraints

$\backslash$table$[[$Constraint Number,Name,Final Value,Shadow Price,Constraint R$.$H$.$ Side,Allowable Increase,Allowable Decrease$],[1,$Cutting and Dyeing Hours Used,$725\mathrm{.}000,0\mathrm{.}000,800\mathrm{.}000,1E+30,75\mathrm{.}000],[2,$Finishing Hours Used,$300\mathrm{.}000,4\mathrm{.}500,300\mathrm{.}000,100\mathrm{.}000,166\mathrm{.}667],[3,$Packaging and Shipping Hours Used,$100\mathrm{.}000,22\mathrm{.}000,100\mathrm{.}000,15\mathrm{.}000,25\mathrm{.}000]]$

$($a$)$ What is the optimal solution, and what is the value of the total profit contribution?

regular glove

catcher's mitt

value

$($b$)$ Which constraints are binding? $($Select all that apply.$)$

cutting and sewing

finishing

packaging and shipping

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$($c$)$ Vvistory are the shadow prices for the resources? Interpret each.

constraint $1$

Each additional hour of cutting and sewing will improve profits by $$22\mathrm{.}00.$

Each additional hour of cutting and sewing will improve profits by $$75\mathrm{.}00.$

Each additional hour of cutting and sewing will improve profits by $$4\mathrm{.}50.$

Additional hours of cutting and sewing will not improve profits.

constraint $2$

Each additional hour of finishing will improve profits by $$22\mathrm{.}00.$

Each additional hour of finishing will improve profits by $$75\mathrm{.}00.$

Each additional hour of finishing will improve profits by $$4\mathrm{.}50.$

Additional hours of finishing will not improve profits.

constraint $3$

Each additional hour of packing and shipping will improve profits by $$22\mathrm{.}00.$

Each additional hour of packing and shipping will improve profits by $$75\mathrm{.}00.$

Each additional hour of packing and shipping will improve profits by $$4\mathrm{.}50.$

Additional hours of packing and shipping will not improve profits.

$($d$)$ If overtime can be scheduled in one of the departments, where would you recommend doing so$?$ cutting and sewing

finishing

packaging and shipping

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