Problem $3-06($Algorithmic$)$

requirements and the profit contribution per glove are given in the following table:

Letting

$R=$ number of regular gloves

$C=$ number of catcher's mitts

leads to the following formulation:

Max $8R+11C,$

$s.t.$

$,2R+\frac{3}{{?}^2}C1200$ Cutting and sewing

$\frac{1}{2^{R+}}250$ Finishing

$\frac{2}{5^C},$

$\frac{1}{8^{R+}}120$ Packaging and shipping

$\frac{1}{5^C},$

The sensitivity report is shown in figure below.

Optimal Objective Value $=,6645\mathrm{.}00000$

Variable

$R$

C

Constraint

$1$

$2$

$3$

Reduced Cost

$0\mathrm{.}00000$

$0\mathrm{.}00000$The sensitivity report is shown in figure below.

Optimal Objective Value $=,6645\mathrm{.}00000$

b$.$ Interpret the ranges in part $($a$).$

As long as the profit per regular glove is between $$6\mathrm{.}88$ and $$13\mathrm{.}75,$ the optimal solution of

gloves will not change.

Or as long as the profit per catcher's mitt is between $$6\mathrm{.}40$ and $$12\mathrm{.}80,$ the optimal solution of

gloves will not change.

The assumption is that

changed at the same time.

answer is zero.

As long as the number of hours available for cutting and sewing $($Constraint $1)$ are

the change in the optimal value of the solution per unit increase in

the right$-$hand side of the constraint isanswer is zero.

As long as the number of hours available for cutting and sewing $($Constraint $1)$ are

the change in the optimal value of the solution per unit increase in

the right$-$hand side of the constraint is

As long as the number of hours available for finishing $($Constraint $2)$ are

the change in the optimal value of the solution per unit increase in the right$-$

hand side of the constraint is

As long as the number of hours available for packaging and shipping $($Constraint $3)$ are

the change in the optimal value of the solution per unit

increase in the right$-$hand side of the constraint is

places. Enter $"0"$ if your answer is zero.

Amount: $