Composite Printing Company currently leases its only copy machine for $ $1500$ a month. The company is considering replacing this leasing agreement with a new contract that is entirely commission based. Under the new$$ agreement, Composite would pay a commission for its printing at a rate of $ $20$ for every $500$ pages printed. The company currently charges $$$$0\mathrm{.}30$ per page to its customers. The paper used in printing costs the company $ $0\mathrm{.}06$ per page and other variable$$ costs, including hourly$$ labor, amount to $ $0\mathrm{.}08$ per page. $1.$

What is the$$ company's breakeven point under the current leasing$$ agreement? What is it under the new$$ commission$-$based agreement?

$2.$

For what range of sales levels will Composite prefer$($a$)$ the fixed lease agreement and$($b$)$ the commission$$ agreement?

$3.$

Composite estimates that the company is equally likely to sell $19000,29000,39000,49000,$ or $59000$ pages of print. Using information from the original$$ problem, prepare a table that shows the expected profit at each sales level under the fixed leasing agreement and under the$$ commission$-$based agreement. What is the expected value of each$$ agreement? Which agreement should Composite $$choose$?$