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 $7.50 per yard, and the cost of the professional grade material is $9.00 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.

\begin{tabular}{|c|c|c|c|c|c|} \hline & \multirow{2}{*}{ Standard } & \multirow{2}{*}{ Professional } & & & \\ \hline & & & & & \\ \hline \multicolumn{6}{|l|}{ Unit Cost } \\ \hline & & & Resources & & Resources \\ \hline & \multicolumn{2}{|c|}{ Resource Requirements } & Used & & Available /Required \\ \hline Minimum Carbon & & & & >= & \\ \hline Maximum Kevlar & & & &