The problem now is to decide which contractor to choose. B has indicated that for another $20 million he could do the job in 18 months, and you have said that you would be indifferent between that and the original proposal. In talking with C, you have indicated that you would just as soon pay her an extra $4 million if she could get the job done in 26 months. Who gets the job?

Question: The question is incomplete. See the full question below and the answer.

You are an up-and-coming developer in downtown Seattle and are interested in constructing a building on a site you own. You have collected four bids from prospective contractors. The bids include both a cost ($millions) and time to completion (months):

Contractor    Cost           Time

A                   100             20

B                    80              25

C                    79               28

D                   82                26

The problem now is to decide which contractor to choose. B has indicated that for another $20 million, he could do the job in 18 months, and you have said that you would be indifferent between that bid and the original proposal. In talking with C, you have indicated that you would just as soon pay her an extra $million if she could get the job done in 26 months. Who gets the job? Explain your reasoning. (It may be convenient to plot the four alternatives on a graph.)

See the explanation for the answer and find attached of the graph.

Explanation:

So we draw a regression line of Time vs Cost and best fit a curve based on the data given, given in the above figure. The four alternatives are marked in the figure as well. Our main objective is to reduce both time and cost, but that might not be possible So the best thing would be to look for alternatives which lie below the line. If C gets an extra million, then that point would come below the regression line, and it would be a better alternative than D, because for the same time we are getting the job done at a cheaper cost.

Also if B is paid extra 20 million, that point also comes below the regression line, and hence will be a better alternative than A because for the same cost again we are getting the job done earlier. We need to choose between B and C. Now in order to optimise both cost and time, we need to choose a point close to the middle point of the regression line segment in 1st quadrant. We see that C is much more closer to the middle point and hence seems like a better option.

So we choose C as our contractor if we consider B's alternative bid, but if we do not consider B's alternative bid and stick to the original one, we choose B as our contractor.