Problem $6$:

Bicycle Frame Production. 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:

Standard Grade Professional Grade

Carbon fiber $10\%30\%$

Kevlar $6\%12\%$

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

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

weight specification, a total of $30$ yards of material must be used for each frame.

Thus!!!

$20\%$ of $30$ yards $=6$ yards... minimum for carbon..

$10\%$ of $30$ yards $=3$ yards... MAXIMUM for Kevlar

Standard grade plus Professional Grade MUST $=30$

Solve for the optimum solution and minimal cost $/$ bicycle frame.