Q1. (Total 40 points) A manufacturing firm is considering the following capacity planning approach in the...

 

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Q1. (Total 40 points) A manufacturing firm is considering the following capacity planning approach in the production of their new product. The variable cost and fixed cost are provided as below. Each machine can produce only 2000 units/year, and the firm can buy up to 2 machines. The firm can sell the product at only $34/unit. The variable cost is $22/unit. Fixed costs indicated for 2 machines is not the incremental cost, but the total fixed cost. For example, 2-machine has a total fixed cost (FC) of $12000/yr, not $20000. Output Range/year 0-2000 (1 machine) 2000-4000 (2machines) FC/year $8,000 $12,000 a) Calculate all the breakeven points for both the 1-machine option and the 2-machine option. (10 points) b) Suppose that there is no penalty cost for lost sales. Determine the best decision making (i.e., either one machine or two-machine option is the best) for all possible demand volumes in the range of (1800, 4000]. (30 points) Q2. (Total 60 points) The Fast Shop Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash register and the operator is the channel in this waiting line system; the customers who line up at the counter to pay for their selections form the waiting line. Customers arrive at a rate of one every 3 minutes according to a Poisson distribution, and service times are exponentially distributed, with a mean rate of 30 customers per hour. a) The market manager wants to determine the following for this waiting line system: (4*6 = 24 points) I. Probability of no customers in the system II. Average number of customers in the total system III. Average time spent in the system per customer IV. Probability that there are more than 2 customers waiting in line Q1. (Total 40 points) A manufacturing firm is considering the following capacity planning approach in the production of their new product. The variable cost and fixed cost are provided as below. Each machine can produce only 2000 units/year, and the firm can buy up to 2 machines. The firm can sell the product at only $34/unit. The variable cost is $22/unit. Fixed costs indicated for 2 machines is not the incremental cost, but the total fixed cost. For example, 2-machine has a total fixed cost (FC) of $12000/yr, not $20000. Output Range/year 0-2000 (1 machine) 2000-4000 (2machines) FC/year $8,000 $12,000 a) Calculate all the breakeven points for both the 1-machine option and the 2-machine option. (10 points) b) Suppose that there is no penalty cost for lost sales. Determine the best decision making (i.e., either one machine or two-machine option is the best) for all possible demand volumes in the range of (1800, 4000]. (30 points) Q2. (Total 60 points) The Fast Shop Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash register and the operator is the channel in this waiting line system; the customers who line up at the counter to pay for their selections form the waiting line. Customers arrive at a rate of one every 3 minutes according to a Poisson distribution, and service times are exponentially distributed, with a mean rate of 30 customers per hour. a) The market manager wants to determine the following for this waiting line system: (4*6 = 24 points) I. Probability of no customers in the system II. Average number of customers in the total system III. Average time spent in the system per customer IV. Probability that there are more than 2 customers waiting in line

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01 a 1machine breakeven point Fixed costSelling Price Variable Cost 80003422 800012 2000 u... View the full answer