$$McBurger$,$ Inc., wants to redesign its kitchens to improve productivity and quality. Three$$ designs, called designs$$ K$1,$ K$2,$ and$$ K$3,$ are under consideration. No matter which design is$$ used, daily production of sandwiches at a typical McBurger restaurant is for $600$ sandwiches. A sandwich costs $$1\mathrm{.}50$ to produce.$$ Non$-$defective sandwiches$$ sell, on the$$ average, for $3$$$\mathrm{.}10$ per sandwich. Defective sandwiches cannot be sold and are scrapped.

The goal is to choose a design that maximizes the expected profit at a typical restaurant over a$300-$day period. Designs$$ K$1,$ K$2,$ and K$3$ cost $$$$115,000,$ $$120,000,$ and $$$$170,000$ respectively.

Under design$$ K$1,$ there is a $\mathrm{.}80$ chance that $90$ out of each $100$ sandwiches are$$ non$-$defective and a $\mathrm{.}20$ chance that $70$ out of each $100$ sandwiches are$$ non$-$defective. Under design$$ K$2,$ there is a $\mathrm{.}85$ chance that $90$ out of each $100$ sandwiches are$$ non$-$defective and a $\mathrm{.}15$ chance that $75$ out of each $100$ sandwiches are$$ non$-$defective. Under design$$ K$3,$ there is a $\mathrm{.}90$ chance that $95$ out of each $100$ sandwiches are$$ non$-$defective and a $\mathrm{.}10$ chance that $80$ out of each $100$ sandwiches are$$ non$-$defective.

Part $2$

The expected profit level of design K$1$ is $$$ $.$The expected profit level of design K$2$ is $$$ $.$ The expected profit level of design K$3$ is $$$