Assignment1 - Solutions.pdf - IMSE 4116 Operations Planning and Control Fall 2017 Solution for Assignment 1 1[15marks A manufacturing company is

Assignment1 - Solutions.pdf - IMSE 4116 Operations Planning...

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IMSE 4116 Operations Planning and Control Fall, 2017 Solution for Assignment 1 1. [15marks] A manufacturing company is planning to produce a new product, but this new product requires the purchase of a new machine. Two machines, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $80,000 for A and $60,000 for B; variable costs per unit of the product would be $20 for A and $22 for B; and revenue per unit would be $30. a. Determine each alternative’s break -even point in units. b. At what volume of output would the two alternatives yield the same profit? c. If expected annual demand is 12,000 units, which alternative would yield the higher profit? Ans: a. ? ?𝐸𝑃 ? = 80000 ∕ (30 − 20) = 8000 ? ?𝐸𝑃 ? = 60000 ∕ (30 − 22) = 7500 b. Profit = ? × ? − (𝐹𝐶 + 𝑣 × ?) The two alternatives yield the same profit when 30? − (80000 + 20?) = 30? − (60000 + 22?) ? = 10000 c. Profit for A = 30 × 12000 − (80000 + 20 × 12000) = 40000 Profit for B = 30 × 12000 − (60000 + 22 × 12000) = 36000 Purchase of machine A yields the higher profit. 2. [15marks] At a coffee shop, there is only one cashier and the time for her to finish an order is exponentially distributed. Customers arrive at the coffee shop according to a Poisson process. The cashier realizes that 25% of her time is idling (i.e., not serving a customer). Suppose that tomorrow there is a promotion of a new coffee product and it is expected to attract 15% more customers to the coffee shop. a. What is the average number of people at the coffee ordering counter (including the one who is placing an order, if any) tomorrow? b. What is the average queue length at the coffee ordering counter tomorrow? c. What is the probability that there are more than four people in the queue waiting for ordering coffee tomorrow?
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