evelopment projects done by Standalone Products are subsidized by a government grant program. The program pays $30$ percent of the total cost of the project $($costs ummed without discounting; i$.$e$.,$ the interest rate is zero$),$ half at the beginning of the project and half at the end, up to a maximum of $$100,000.$ There are two projects eing considered. One is a customized checkweigher for cheese products and the other is an automated production scheduling system. Each project has a service life five years. Costs and benefits for both projects, not including grant income, are shown below. Only one can be done, and the grant money is certain. Standalone roducts has a MARR of $10$ percent for projects of this type. Using an appropriate rate of return method, which project should be chosen?

$\backslash$table$[[,$Checkweigher,Scheduler$],[$irst cost$,$$$30,000,$$$9,000$

Aline has three contracts from which to choose. The first contract will require an outlay of $$100,000$ but will return $$165,000$ one year from now. The second contract requires an outlay of $$210,000$ and will return $$330,000$ one year from now. The third contract requires an outlay of $$270,000$ and will return $$402,000$ one year from now. Only one contract can be accepted. If her MARR is $25$ percent, which one should she choose?

For the increment from the do$-$nothing alternative to the first contract, the IRR is percent. For the increment from the first contract to the second contract, the IRR is percent. For the increment from the second contract to the third contract, the IRR is percent. Therefore, $($Type integers or decimals rounded to one decimal place as needed.$)$ should be chosen.