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P$5.$ BUSINESS APPLICATION State Street Lending processes loan applications. The manager of the loan department has established a policy of charging a $$250$ fee for every loan application processed. Variable costs have been projected as follows: loan consultant's wages, $$15\mathrm{.}50$ per hour $($a loan application takes $5$ hours to process$)$; sup$-$plies, $$2\mathrm{.}40$ per application; and other variable costs, $$5\mathrm{.}60$ per application. Annual fixed costs include depreciation of equipment, $$8,500$; building rental, $$14,000$; promotional costs, $$12,500$; and other fixed costs, $$8,099.$

REQUIRED

$$Using the contribution margin approach, compute the number of loan applications the company must process to $($a$)$ break even and $($b$)$ earn a profit of $$14,476.$

$$Using the same approach and assuming promotional costs increase by $$5,662,$ compute the number of applications the company must process to carn a profit of $$20,000.$

$$Assuming the original information and the processing of $500$ applications, compute the loan application fee the company must charge if the targeted profit is $$41,651.$

$$The maximum number of loan applications that the department can process is $750.$How much more can be spent on promotional costs if the highest fee tolerable to the customer is $$280,$ if variable costs cannot be reduced, and if the targeted profit is $$50,000?$