On a beautiful Saturday morning. you and your friend go to the state fair ofTaxas. Within the park. you can buy everything using either coupon or cash (different from the state fair of Texas). I coupon can be used as 1 dollar. The coupon vender is only available at the front gate. where you can buy each coupon for only $0.8. You are not sure about the total amount you will spend in the park. but you are able to estimate its distribution as follows: Total Spending Probability Distribution Function 30 0.3 40 0.4 50 0.3 In addition, we make the following assumptions: I You won't return and buy additional coupons once you enter the park. If you run out of coupons, you won't stop spending - you simply use cash. For example. suppose you buy 30 coupons, and your total spending in the park is 50. In this case. you spend all your coupons and $20 cash in addition. I At the end of the day. the coupons that you haven't used can be refunded at a price of $0.5 per coupon. a. (3 points) Complete the third column of the table above. b. (3 points] Suppose you buy 40 coupons at the gate, and you spend 50 (including 4\" coupons and SID cash) in the park. How much cash (in dollar value. including the cash you spend to buy cou ons] do ou s end in total? c. (4 points) You need to decide how many coupons to buy at the gate. Compute your underage and overage costs. explain. d. (5 points) Based on your answer to the previous question. how many coupons should you buy at the gate'? e. (5 points) Based on your answer to the previous question, how much do you expect to save, compared with not buying coupon at all (and use cash for all the spending}? f. (5 points) The vendor starts selling coupons at 8am. When you arrive at the vendor at 8am, there are already 5 customers waiting in the line. It takes 1 minute for each customer to get hisfher coupons from the vendor. You are very impatient and each minute of waiting (including being served by the vendor) incurs $1.0 unhappiness cost for you. Are you still going to buy eoupon'? Compute your expected unhappiness cost: Compare it with the expected saving from buying coupon (your answer for the previous question)