The Elon Rust Company estimates the annual demand for the new energy$-$save refrigerator with the following demand levels and associated probabilities:

$90,000$ units $(18\%$ probability$)$

$102,000$ units $(35\%$ probability$)$

$107,000$ units $(19\%$ probability$)$

$141,000$ units $(10\%$ probability$)$

$151,000$ units $(8\%$ probability$)$

Assume the following for your calculations:

Lost business $($stockout$)$ costs are $$120,000$ per thousand units.

The cost to build $1,000$ units of capacity is $ $25,000$

Consider the capacity cushion $=100\%-$ utilization

Questions:

If the capacity is $107,000$ units how much of a capacity cushion is there?

What is the average utilization of the plant?

Select the CORRECT answers to the above mentioned questions:

Group of answer choices

The capacity cushion is $15\%$ and the average utilization of the plant is $81\%$

The capacity cushion is approximately $8\mathrm{.}03\%$ and the average utilization of the plant is $63\%$

The capacity cushion is $19\%$ and the average utilization of the plant is $81\%$

The capacity cushion is approximately $8\mathrm{.}03\%$ and the average utilization of the plant is $91\mathrm{.}97\%$