Not$-$for$-$Profit Applications

Determine the solutions to each of the following independent cases:

$($a$.)$ Collings College has annual fixed operating costs of $$20,000,000$ and variable operating costs of $$2,400$ per student. Tuition is $$12,000$ per student for the coming academic year, with a projected enrollment of $2,000$ students. Expected revenues from endowments and federal and state grants total $$400,000.$ Determine the amount the college must obtain from other sources.

$Answer

$($b$.)$ The Collings College Student Association is planning a fall concert. Expected costs $($renting a hall, hiring a band, etc.$)$ are $$15,000.$ Assuming $2,000$ people attend the concert, determine the break$-$even price per ticket. How much will the association lose if this price is charged and only $1,500$ tickets are sold? $($Do not use a negative sign with your answer.$)$

$Answer

$($c$.)$ City Hospital has a contract with the city to provide indigent health care on an outpatient basis for $$125$ per visit. The patient will pay $$10$ of this amount, with the city paying the balance $($$$115).$ Determine the amount the city will pay if the hospital has $5,000$ patient visits.

$Answer

$($d$.)$ A civic organization is engaged in a fund$-$raising program. On Civic Sunday, it will sell newspapers at $$2\mathrm{.}50$ each. The organization will pay $$1\mathrm{.}75$ for each newspaper. Costs of the necessary permits, signs, and so forth are $$750.$ Determine the amount the organization will raise if it sells $3,000$ newspapers.

$Answer

$($e$.)$ Christmas for the Needy is a civic organization that provides Christmas presents to disadvantaged children. The annual costs of this activity are $$10,000,$ plus $$20$ per present. Determine the number of presents the organization can provide with $$30,000.$

Answer

presents