A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made

of both steel and aluminum. The company has available $68,000$ units of steel and $31,500$ units of

aluminum. The racing, touring, and mountain models need $17,20,$ and $34$ units of steel, and $9,$

$18,$ and $15$ units of aluminum, respectively. Complete parts $($a$)$ through $($d$)$ below.