QUESTION $4(20$ Marks$)$ Precision Bolts Ltd is a mid$-$sized manufacturing company located in Gauteng, South Africa. The plant specialises in producing standardised steel bolts for use in the construction, automotive, and mining sectors$.$ The organisation is evaluating the performance capability of its main production line, which manufactures hex$-$head steel bolts. For the third week of October, the facility produced $148,000$ bolts which is $84\mathrm{.}57\%$ of the plant$$s weekly effective capacity. The production line operates $7$ days a week, running three $8-$hour shifts per day. The line was originally designed to produce the M$10$ high$-$tensile hex bolt at a rate of $1,200$ units per hour. The new manufacturing director, George, has decided to expand the organisations manufacturing capacity by installing an additional production line. With this expansion, the company will operate two production lines, each running $7$ days a week, $3$ shifts per day, and $8$ hours per shift. The combined effective capacity of the two lines is $300,000$ bolts per week. However, the addition of the second line is expected to reduce overall system efficiency to $85\%$ due to increased coordination complexity and resource sharing. $4\mathrm{.}1$ Determine the design capacity, utilisation and efficiency for the plant for the third week of October. $(12$ Marks$)4\mathrm{.}2$ Using the changes implemented by George, determine the new utilisation for the manufacturing plant using the new effective capacity.