$3.$ A manual assembly line is to be designed to make a small consumer product. The work elements, their times, and precedence constraints are given in the table below. The workers will operate the line for $400$ min per day and must produce $300$ products per day. Because of the variability in the time required to perform the assembly operations, it has been determined that the tolerance time should be $1\mathrm{.}5$ times the cycle time of the line.$($a$)$ Determine the ideal minimum number of workers on the line.$($b$)$ Use the Ranked Positional Weights method to balance the line.$($c$)$ Compute the balance delay for your solutionElementTime IePreceded by:ElementTime TePreceded by:$10\mathrm{.}4$ m$1$n$60\mathrm{.}2$ min$320\mathrm{.}7$ min$10\mathrm{.}3$ min$430\mathrm{.}5$ min$80\mathrm{.}9$ mi