An operator needs $53$ seconds to unload and load a machine, and $15$ seconds to reach the next workstation. Each machine runs automatically for $3\mathrm{.}6$ minutes and costs $25\mathrm{.}8/$hour to run. Given a base part cost of $1\mathrm{.}68$ and an operator rate of $33\mathrm{.}5/$hour$,$ calculate:

a$)$

How many machines should be assigned to an operator for lowest cost?

b$)$

Calculate the production rate and visualise the result in a man$-$machine diagram.

c$)$

The management wants a profit of $10\%$ on this product. Assuming no products are rejected during quality control, what should be the selling price of the product?

d$)$

What is the utilization of the operator and the machines?