Student tuition at Boehring University is $$$$180$ per semester credit hour. The state supplements school revenue by $$$$90$ per semester credit hour. Average class size for a typical $3-$credit course is $55$ students. Labor costs are $$$$4,200$ per$$ class, materials costs are $$$$21$ per student per$$ class, and overhead costs are $$$$26,000$ per class. The multifactor productivity ratio currently is $1\mathrm{.}42$ and the labor productivity ratio is $$$$198\mathrm{.}88$ per hour if the instructors work on an average of $14$ hours per week for $16$ weeks for each $3-$credit class of $55$ students.

Coach Bjourn Toulouse led the Big Red Herrings to several disappointing football seasons. Only better recruiting will return the Big Red Herrings to winning form. Because of the current state of the$$ program, Boehring University fans are unlikely to support increases in the$$ $$192$ season ticket price. Improved recruitment will increase overhead costs to $$$$33,000$ per class section from the current $$$$26,000$ per class section. The$$ university's budget plan is to cover recruitment costs by increasing the average class size to $80$ students. Labor costs will increase to $$$$7,200$ per $3-$credit course. Material costs will be about $$$$35$ per student for each $3-$credit course. Tuition will be $$$$250$ per semester$$ credit, which is supplemented by state support of $$$$90$ per semester credit.

Part $2$

a$.$ The multifactor productivity ratio with the$$ university's plan to meet the expenses related to improving recruitment is