Applied Technology, Inc. $(ATI),$ produces bicycle frames using two fiberglass materials that

improve the strength$-to-$weight ratio $of$ the frames. The cost $of$ the standard grade material $is$

$$7\mathrm{.}50$ per yard and the cost $of$ the professional grade material $is$ $$9\mathrm{.}00$ per yard. The standard and

professional grade materials contain different amounts $of$ Fiberglass, Carbon Fiber, and Kevlar

$as$ shown $in$ the following table:

ATI signed a contract with a bicycle manufacturer $to$ produce a new frame with a carbon fiber

content $ofat$ least $20\%$ and a Kevlar content $of$ not greater than $10\%.To$ meet the required

weight specification, a total $of30$ yards $of$ material must $be$ used for each frame.

Formulate a linear program problem $to$ determine the number $of$ yards $of$ each grade $of$

fiberglass material that ATI should use $in$ each frame $in$ order $to$ minimize total cost.

Define the decision variables and indicate the purpose $of$ each constraint.

Solve the $LP-$problem using $QM.$

Three output illustrations required for submission:

$a.$ The Graph

$b.$ The Solution

$c.$ The Intervals

State the optimal Solution and the Minimum Cost associated with $it.$

State the intervals for the coefficients $of$ the objective function.

Identify one $of$ the Essential Constraints.

$a.$ State the interval for the right hand side $of$ this constraint.

$b.$ How would increasing the current value affect the minimum cost?

$c.$ How would decreasing the current value affect the minimum cost?

$[You$ may need $to$ edit the $LP-$problem $to$ confirm your suspicion.$]$