$3\mathrm{.}14$ The table below presents production data for three batches of parts processed through a batch production plant. Production rates $(R_p)$ are given in parts per hour. Utilization fractions $(f)$ are the fractions of time during the $40-$hr week that the machine is devoted to the production of these parts. The parts do not proceed through the machines in the same order. Determine $($a$)$ weekly production rate, $($b$)$ workload, and $($c$)$ average utilization of this set of equipment. A spreadsheet calculator is recommended for this problem.

$\backslash$table$[[,$Machine $1,$Machine $2,$Machine $3,$Machine $4],[$Part$,R_{p1},f_1,R_{p2},f_2,R_{p3},f_3,R_{p4},f_4$