A state government has an affiliated day$-$care center for kids. The center provides three different programs for infants, toddlers, and preschool kids. Tuition is charged weekly. The center runs at full capacity, which is $30$ infants, $30$ toddlers and $40$ preschool kids. The center pays a monthly rent of $$4,000$ for the building they use. The center hires an executive director, a coordinator, an accountant, and a staff member working with maintenance and cleaning. Their annual salaries are $$60,000,$ $$50,000,$ $$40,000,$ and $$35,000.$ State laws require that the student$-$to$-$teacher ratio should be $5$:$1$ for infants, $6$:$1$ for toddlers, and $10$:$1$ for preschool kids. Each teacher gets an annual salary of $$50,000.$ The expenses for daily activities per kid per day for the three programs are $$10($infant$),$ $$12($toddler$),$ and $$15($preschool kids$).$ Electricity, depreciations, and other expenses run up to around $$2,000$ in total per month. Identify all the items of fixed $.$ The center decides to charge the same weekly tuition for each kid in all the three programs $($infants$,$ toddlers, and preschool kids$).$ Calculate the break$-$even price per kid per week. If state employees get a $10\%$ discount on the tuition, and the center estimates that $90\%$ of the kids come from families of state employees, what is the full tuition price per week at break$-$even? $($Hint: calculate the weighted break$-$even price for both state employees and non$-$state employees$).$If state employees get a $10\%$ discount on the tuition, and the center estimates that $90\%$ of the kids come from families of state employees, what is the full tuition price per week at break$-$even? $($Hint: calculate the weighted break$-$even price for both state employees and non$-$state employees$).$