3. An airplane has 15 seats and 15 passengers, each with an assigned seat (passenger \( k \) assigned to seat \( k \)). Passenger No.1 boards first but has lost the boarding pass and chooses a seat uniformly at random. Passengers No.2 through No.14 board in order: each takes their assigned seat if available; otherwise, they choose a remaining seat uniformly at random. Passenger No.15 boards last. What is the exact probability that Passenger No.15 sits in the assigned seat (seat No.15)? (10%)

(Note: You are asked to answer in percentages, counted to two decimal places.)

(1) Assuming that A1, A2, and A3 are distinct sculptures, calculate the total number of ways that the 10 sculptures can be arranged on the pedestals while satisfying all three conditions. (20%)

(2) Assuming that A1, A2, and A3 are the same sculpture, calculate the total number of ways that the 10 sculptures can be arranged on the pedestals while satisfying all three conditions. (20%)

(1) STARK bought a 2,000-acre land for $8,215,300 and divided it into 200 equal size lots. As the lots are sold, they are cleared at an average cost of $5,210. Storm drains and driveways are installed at an average cost of $8,000 per site. Sales commissions are 10% of selling price. Administrative costs are $850,000 per year. The average selling price was $160,000 per lot during 2019 when 50 lots were sold. During 2020, STARK bought another 2,000-acre land and developed it exactly the same way. Lot sales in 2020 totaled 300 with an average selling price of $160,000. All costs were the same as in 2019. Compute the operating income for both years using both absorption and variable costing methods (Show computations). Explain why operating income is (or not) the same under the two costing methods in 2019 and 2020, respectively. (8%)

(2) HAWKEYE sells hot dogs for $1.35. Variable costs are $1.05 per unit with fixed production costs of $90,000 per month at a level of 400,000 units. Fixed administrative costs total $30,000. Sales average 400,000 units per month, with planned production of 400,000 hot dogs. What are breakeven unit sales under absorption costing if average sales are 498,000 and planned production is changed to 500,000? Show computations. (5%)

(3) WANDA orders most of its items in lot sizes of 10 units. Average annual demand per side of beef is 720 units per year. Ordering costs are $25 per order with an average purchasing price of $100. Annual inventory carrying costs are estimated to be 40% of the unit cost. Compute the annual cost savings if the shop changes from an order size of 10 units to the economic order quantity. Show computations. (5%)

(1) Prepare a production cost worksheet using the FIFO method. (12%)

(2) "In job costing, the costs of normal spoilage that occur while a specific job is being done are charged to the specific job." Do you agree? Explain. (5%)

3. APPLE is in need of a microcomputer network for its staff. The company uses straight-line depreciation for all capital assets. Annual required rate of return is 14%. The company has received three proposals, with related facts as follows:| | Required:Compute the payback period, net present value, and accrual accounting rate of return with initial investment, for each proposal. Show computations. Rank each proposal 1, 2, and 3 using each method separately. Which proposal is best? Why? (15%)

(1) What was the full cost per unit? What was the selling price? (12%)

(2) Taipei is considering increasing the annual spending on advertising by $175,000. The managers believe that the investment will translate into 10% increase in unit sales. Should Taipei make the investment? Show your calculations. (8%)

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