Presently, one operator is tending five identical machines. Each machine is used to produce similar products. With $5$ machines it has been observed that during a cycle a total of $20$ machine$-$minutes is consumed in machines waiting for service to begin. In the past, it was observed that the operator was idle for $10$ minutes each cycle when assigned to tend $3$ machines. If machining time is $25$ minutes and independent operator time is $1$ minute per machine cycle, what is the value for concurrent activity? If $C_1$ equals $$\frac{4}{?}$ hour and $C_2$ equals $$\frac{6}{?}$ hour, what is the economic assignment? What is the value of the minimum cost per unit produced?

A construction firm is working on a roadway for which dump trucks and power shovels are the primary equipment being used. Time studies reveal the following time values $($minutes$)$

$\backslash$table$[[$Time to load a truck,$15],[$Travel time to dumping point,$15],[$Dumping time,$3],[$Return time,$13]]$

$($a$)$ What is the minimum number of trucks that will prevent idle time on the part of the power shovel?

$($b$)$ Suppose that it costs $$25$ per hour to operate the power shovel and $$15$ per hour to operate each truck. How many trucks should be assigned to the job to minimize the cost per truck load hauled?

$($c$)$ Construct a man$-$machine chart for the most economical arrangement between dump trucks and the power shovel.