Question

A operations  manager of znc furniture ,you must make a decision about adding a line of rustic  furniture. In discussing the possibility with your sales manager  YAmamoto  Rene , you decide that there will definitely be a market and that your firm should enter that market however become rustic furniture has a different finish than your standard offering, you decide you need another process line. There is no doubt in your mind about the decision and you are sure that you should have a second process. But you do question how large to make it. A large process line is going to cost $425,000 a small process line will cost $350,000. The question, therefore  is the demand for rustic furniture. After extensive discussion with the Mr Yo and  Richard of Richard market Research, inc,  you determine that the best estimate you can make is that there is a two-out-of three chance of high demand resulting in $650,000 profit from sales and a one out of three chance of low demand resulting in $ 325,000 profit from sales. 

With a large process line you could handle the high figure of $650,000 however with a small process line you could not and would be forced to expand ( at a cost $175,000) , after which time your profit from sales would be $500,000 rather than the $650,000 because of the lost time in expanding the process. If you do not expand the small process, your profit from sales would be held to$425,000.I you build a small process and the demand is low you can handle all of the demand. 

The best option is to open a

large line or a small line? , with an expected value of $.........(round round your response to the nearest whole number)

Answer 1

There are two key choices for decision. They are large and small lines.

Large line

If you build a large line it will cost 425000. There is a 2/3 chance of profit from sales 650000. This means the net profit is 650000-425000 = 225000. Also there is a chance of only 325000. This will result in loss of 425000-325000 = 100000. This indicates that expected value of the large line is (2/3)*225000 + (1/3)*(-100000) = 116666.67

Small line

In case we build a small line it will cost 350000. If the demand is low (chance of 1/3) then the profit will be 325000. This means the loss is 25000.

In case we build a small line and the demand is high, we have two further choices. If we do nothing, it will result in a profit of 425000. This means the net profit will be 425000-350000 = 75000. On the other hand if we choose to extend to a large line then it will be 500000 – 175000 – 350000 = -25000. This means if the demand is high the best option will be to choose not to extend. This means that the probability of 2/3 and the corresponding payoff is 75000

The expected value of the small line is (1/3)*(-25000) + (2/3)*(75000) = 41666.67

Comparing the two the better choice is a large line as it provides a higher expected value.

The best option is to open a large line with an expected value of $116667