DO NOT COPY SOMEONE ELSE'S ANSWER. I AM NOT STUPID, I CAN EASILY TELL. ESPECIALLY WHEN THE ANSWER IS WRONG.

Please SHOW ALL WORK and formulas and stuff! And don't just copy/paste someone else's answer please, I want someone who knows the right answer. Thank you.

Q2. The UTD cafeteria offers scones for $1.5 each from 8am to 3 pm. The scones are ordered from their supplier at the start of each day and delivered before the store opens. The supplier charges 75 cents per scone. If at 3 pm, some scones are left unsold, the cafeteria people sell off the remaining scones for 50 cents each. Assume that all leftover scones are always sold by 4 pm when the cafeteria closes. If a customer asks for a scone before 3 pm but the cafeteria has run out, the customer always buys a bag of chips for $1 instead (after 3 pm, the customer does not buy anything instead). Assume the chips are always in stock and they are purchased from the same supplier for 40 cents each. Demand for scones before 3 pm at the cafeteria is variable but can only take values between 40 and 50, with probabilities given in the following table. Number of customers Probability 40 0.05 41 0.05 42 0.15 43 0.2 44 0.15 45 0.1 46 0.1 47 0.1 48 0.05 49 0.025 50 0.025 a. What is the expected number of customers who want to buy a scone on a given day? (1 points) b. Yesterday the cafeteria ordered 45 scones, and 49 customers came wanting to buy a scone between 8 am and 3 pm. What was their profit (including, if any, the profit on chips sold instead of scones)? (1 points) c. How much is the underage cost? (2 points) d. How much is the overage cost? (2 points) e. What is the optimal number of scones to order at the start of each day? (2 points) f. Given the order quantity in part e, what is the probability that the cafeteria cannot satisfy all the demand for scones before 3 pm? (2 points)