Freddy owns a taxicab company and is trying to find the most economical method of handling incoming calls. He currently has a couple of employees working the phones, but wonders if there is a better arrangement. His options for the call center are: continue with his own staff, outsource to a large company that specializes in call centers, or use a combination of his own staff and the large company. The annual cost of each option (in thousands of dollars) depends on demand as follows.

Demand

Staffing options high medium low
own staff 30 30 25
outsource 50 25 15
combination 40 30 20

If the demand probabilities are .3, .4, and .3, which decision alternative will minimize the expected cost of the call center?
A) Own staff
B) Outsource
C) Combination

What is the expected annual cost associated with that recommendation?
A) $29,500
B) $35,000
C) $30,000
D) $28,500
E) $30,500

For your recommendation, what is the probability of cost exceeding $35,000?
A) .7
B) .3
C) .6
D) 0

To find the most economical method of handling incoming calls for Freddy's taxicab company, we need to calculate the expected annual cost for each staffing option and compare them.

Step 1: Calculate the expected cost for each staffing option
To calculate the expected cost, multiply each demand level's cost by its corresponding probability and sum them up.

Own Staff:
Expected cost = (high demand cost * high demand probability) + (medium demand cost * medium demand probability) + (low demand cost * low demand probability)
= (30 * 0.3) + (30 * 0.4) + (25 * 0.3)
= 9 + 12 + 7.5
= 28.5

Outsourced:
Expected cost = (50 * 0.3) + (25 * 0.4) + (15 * 0.3)
= 15 + 10 + 4.5
= 29.5

Combination:
Expected cost = (40 * 0.3) + (30 * 0.4) + (20 * 0.3)
= 12 + 12 + 6
= 30

Step 2: Compare the expected costs and determine the most economical option
Looking at the expected costs calculated above, the option with the lowest expected cost is the most economical. In this case, the outsourced option has the lowest expected cost of 29.5, followed by the own staff option with an expected cost of 28.5, and the combination option with an expected cost of 30.

Therefore, the decision alternative that will minimize the expected cost of the call center is the outsourced option (B) - Outsourced.

Step 3: Calculate the probability of cost exceeding $35,000 for the recommended option
To calculate the probability of cost exceeding $35,000 for the outsourced option, we need to sum up the probabilities for high and medium demand.

Probability of cost exceeding $35,000 = high demand probability + medium demand probability
= 0.3 + 0.4
= 0.7

Therefore, the probability of cost exceeding $35,000 for the recommended option is 0.7 (A) - 0.7.

So, the answers to the questions are:
1. Decision alternative: B) Outsource
2. Expected annual cost: B) $29,500
3. Probability of cost exceeding $35,000: A) 0.7