$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

The management of Madeira Computing is considering the introduction of a wearable electronic device with the functionality of a laptop computer and phone. The fixed cost to launch this new product is $$300,000.$ The variable cost for the product is expected to be between $$160$ and $$240,$ with a most likely value of $$200$ per unit. The product will sell for $$300$ per unit. Demand for the product is expected to range from $0$ to approximately $20,000$ units, with $4,000$ units the most likely.

$($a$)$ Develop a what$-$if spreadsheet model computing profit for this product in the base$-$case, worst$-$case, and best$-$case scenarios.

If your answer is negative, use minus sign.

$1)$ Best$-$case profit $$\_\_\_\_\_$

$2)$ Worst$-$case profit $$\_\_\_\_\_$

$3)$ Base$-$case profit $$\_\_\_\_\_$

$($b$)$ Model the variable cost as a uniform random variable with a minimum of $$160$ and a maximum of $$240.$ Model the product demand as $1,000$ times the value of a gamma random variable with an alpha parameter of $3$ and a beta parameter of $2.$ Construct a simulation model to estimate the average profit and the probability that the project will result in a loss.

Round your answers to the nearest whole number.

Average Profit $$\_\_\_\_\_$

Probability of a Loss $\_\_\_\_\_\%$