$$McBurger$,$ Inc., wants to redesign its kitchens to improve productivity and quality. Three$$ designs, called designs$$ K$1,$ K$2,$ and$$ K$3,$ are under consideration. No matter which design is$$ used, daily production of sandwiches at a typical McBurger restaurant is for $500$ sandwiches. A sandwich costs $$1\mathrm{.}30$ to produce.$$ Non$-$defective sandwiches$$ sell, on the$$ average, for $$2\mathrm{.}50$ 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$$ K$1,$ K$2,$ and K$3$ cost $$100,000,$ $$130,000,$ and $$180,000,$ 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 $$$enter your response here. $($Enter your response as a real number rounded to two decimal places.$)$

Part $3$

The expected profit level of design K$2$ is $$$enter your response here. $($Enter your response as a real number rounded to two decimal places.$)$

Part $4$

The expected profit level of design K$3$ is $$$enter your response here. $($Enter your response as a real number rounded to two decimal places.$)$

Part $5$

What is the expected profit level of the design that achieves the maximum expected$300-$day profit$$ level?

Design

$$

K$2$

K$3$

K$1$

achieves the maximum expected$300-$day profit$$ level, with a profit of $$$enter your response here. $($Enter your response as a real number rounded to two decimal places.$)$