The J. P. Atkins Company will soon be introducing a new product. Estimates have been made of the monthly profit that would be generated by this product for each of four alternative values of the monthly production rate, as shown to the right.

Production                       Rate Profit

200.......................................$ 9,500

500........................................22,500

800........................................34,000

1,000....................................40,000

a. Draw a profit graph for this product by plotting the profits for the four production rates and then drawing a smooth curve through the four points by hand. (Start the graph with a profit of 0 at a production rate of 0.)

b. Does the proportionality assumption of linear programming seem to be satisfied reasonably well for this product?

c. To the extent that profit is not strictly proportional to the production rate, does this product have decreasing marginal returns, increasing marginal returns, or neither?

d. Use Excel's curve fitting method to (1) obtain a nonlinear formula with a quadratic form for the profit graph and then (2) construct the graph.