__Problem 1__

A manufacturing plant has reached full capacity. The company must build a second plant—either small or large—at a nearby location. The demand is likely to be high or low. The probability of high demand is 0.8, and low demand is 0.2. If demand is low, the large plant has a present value of $5 million and the small plant, a present value of $10 million. If demand is high, the large plant pays off with a present value of $18 million, and the small plant with a present value of only $9 million (if they do nothing). However, the small plant can be expanded later if demand proves to be high for a present value of $14 million.

**a**. Draw a decision tree for this problem. (Note: if they build a small plant and later in the future demand turns out to be high, then they can make a second decision to either expand or do nothing).

**b.** What should management do to achieve the highest expected payoff?

**c**. If the probabilities of high and low were 0.50 each, recalculate the expected payoffs. Does this change the earlier decision?

__Problem 2__

A company is considering two different manufacturing processes for making a new product. Process #1 is less capital intensive, with fixed costs of $100,000 per year and variable costs of $70 per unit. Process #2 has fixed costs of $500,000 annually, with variable costs of $30 per unit.

- What is the break-even quantity for the two processes?
- If expected demand was estimated to be 8,500 should you select the first process or the second process?

- Operations and Engineering have found a way to reduce the cost of the second process, such that the fixed costs for this process decrease from $500,000 to $400,000 annually. All other costs remain the same
*(1st process fixed = $100,000/year, 1st process variable = $70/unit, 2nd process variable = $30/unit).***What is the new break-even quantity between the two processes? Does this change your decision in part b above?**

__Problem 3__

From the power points of chapter 6 (Constraint Management), solve Application 1 and 2 again using the changed data below. Solve using the Bottleneck-based approach directly.

__Problem 4__

Refer to the Solved Problem 2 in your textbook, (or presentation slides), and resolve it again using the changed data below (D is now 70).

A company is setting up an assembly line to produce 192 units per 8-hour shift. The following table identifies the work elements, times, and immediate predecessors:

Work Element | Time (sec) | Immediate Predecessor(s) | ||

A | 40 | None | ||

B | 80 | A | ||

C | 30 | D, E, F | ||

D | 70 | B | ||

E | 20 | B | ||

F | 15 | B | ||

G | 120 | A | ||

H | 145 | G | ||

I | 130 | H | ||

J | 115 | C, I | ||

Total 765 |

a. What is the desired cycle time (in seconds)?

b. What is the theoretical minimum number of stations?

c. Use the longest task time approach to allocate tasks to work stations and show your solution on the table below.

d. What is the efficiency and balance delay of the solution found?

e. If the company wants to produce more units, which **work station** do you think will be limiting it from future production increases (bottleneck)? *(look at the idle time of each workstation)*

Station | Candidate(s) | Choice | Work-Element Time (sec) | Cumulative Time (sec) | Idle Time |

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