General goal programming can be represented as preemptive and non$-$preemptive expressions. Considering these expressions, answer the following questions:

i

Suppose that the market demand for each product is of a higher priority than balancing the two machines, with no overtime allowed. Further, suppose that the manufacturing company specifies that the number of units produced for Part $1$ in excess of Part $2$ contains the lowest priority among all goals. Using preemptive priority factors, formulate the preemptive goal programming model. $(11\mathrm{.}5)$

ii

Suppose that the market demand for each product has a weight of $2$ and that the number of units produced for Part $1$ in excess of Part $2$ contains a weight of $7.$ Likewise, suppose that balancing the two machines comprises a weight of $3,$ with overtime once again not allowed. Formulate and solve the non$-$preemptive goal programming model. Determine if all the goals are satisfied and motivate your answer. $(9\mathrm{.}5)$