Jumbo James Sells Hotdogs Out of a Cart for $3 $$\begin{array} { c c } \text { Demand Per Day } & \text { Probability } \\\hline 100 & 0.50 \\200 & 0.30 \\300 & 0.20\end{array}$$

Jumbo James sells hotdogs out of a cart for $3.00 each. His cost to purchase and prepare the hotdog is $1.15 each. He operates the small business with very few capital assets and has no place to store unsold hotdogs. For this reason, every evening he sells the unsold hotdogs to a local homeless shelter for $0.50 each. Jumbo James will choose one of the following options as a standard stocking plan: d₁ = 100; d₂ = 150; or d₃ = 200 hot dogs. On any weekday, the demand for hot dogs and the probability of selling them is estimated as follows:
$$\begin{array} { c c } \text { Demand Per Day } & \text { Probability } \\\hline 100 & 0.50 \\200 & 0.30 \\300 & 0.20\end{array}$$
a. Determine the expected value if Jumbo James stocks 200 hot dogs every day.
b. Determine the expected value if Jumbo James decides to stock 150 hot dogs every day.