The Chiplet Corporation is about to launch the production and marketing of a new microchip that is more powerful than anything that is currently on the market. Not surprisingly, the profitability of this microchip will depend greatly on its reception in this highly competitive and fast-moving market. If the sales are fairly low, the company will still be able to make a respectable profit because it will have enough available production capacity to produce the microchip with its current facilities. However, if sales are somewhat higher, the company will need to expand its production facilities, which will have the effect of depressing the profit from the microchip if sales only reach a moderate level. (Fully meeting this demand would still be worthwhile because one of top management's prime goals is to continue increasing the company's market share as it points toward future generations of microchips already under development.) Fortunately, if sales reach a relatively high level, the profit from the microchip will become very substantial. The following table shows the estimated profit for various levels of sales over the short lifetime of this microchip.
Sales Profit
(millions of dollars)
0........................................0
100,000..............................15
200,000..............................18
300,000..............................13
400,000...............................4
500,000...............................1
600,000...............................6
700,000..............................30
800,000..............................70
a. Draw a profit graph for this microchip by plotting the profits for the various sales levels and then drawing a smooth curve that passes through (or very near) these points.
b. Does the microchip have decreasing marginal returns, increasing marginal returns, or neither?
E* c. Use Excel's curve fitting method to (1) obtain a nonlinear formula with a quadratic form (a polynomial of order 2) for the profit graph and then (2) construct the graph.
E* d. Repeat part c when using the Excel option of a polynomial of order 3 instead of order 2.
e. Which of the Excel options used in parts c and d does a better job of fitting the profit graph to the data?