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(ISMT162)2006fall_Quiz_1_ISMT162_B[1].pdf
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Quiz 1
Time: 9:00am C 9:50am
(9 Questions, 20 Points)

Note: Each question has 5 choices. There is only ONE correct answer for each question. You are required to write down the reason or the procedure to find your choice on the sheet. If you only give the correct answer without reasonable explanation or the procedure, you obtain 0.5 point for each question.

Name: Student No.:


Question 1. (2 points) A manager must decide how many machines of a certain type to purchase. Each machine can process 100 customers per day. One machine will result in a fixed cost of $2,000 per day. Variable costs will be $20 per customer, and revenue will be $45 per customer. Assume that estimated demand is 90 to 120 customers per day. If two machines result in a fixed cost of ________ per day, the manager should purchase two machines.

(a) $3,800; (b) $2,500; (c) $2,250; (d) $3,500; (e) $3,000.
Answer: c
Reason or Procedure:



Key: The smallest fixed cost is the best.

For any fixed cost F, the break even point is given by
Q = F/(45-20).

When F=2250, Q= 90. Even if demand is only 90, the managers profit is still not negative.













Question 2. (2 points) Consider the following linear programming problem:
Maximize

Subject to




,

Which of the following is a feasible solution?
(a) ; (b)

;


(c) ; (d)

;
(e) .

Answer: e
Reason or Procedure:

For (a), x2<-1, the third constraint is violated.
For (b), the non-negativity constraint for x2 is not satisfied;
For (c), the first constraint is not satisfied;
For (d), the second constraint is not satisfied;
For (e), all constraints are satisfied;
























Question 3. (2 points) The graphic solution of the LP defined in Question 2 is given as below. From the graphic, what is the optimal solution?


(a) ; (b)

;
(c) ; (d)

;
(e) .



Answer: e
Reason or Procedure:




From the graphic, we observe that the optimal corner point is the cross point of the two lines:


This leads to the optimal solution is
.













Question 4. (2 points) A logistic provider plans to have a new warehouse built to handle increasing demands for its services. Although the company is unsure of how much demand there will be, it must decide now on the size (large or small) of the warehouse. Preliminary estimates are that if a small warehouse is built and demand is low, the monthly income will be $700