Question

The following table shows the estimated daily profit from a new product for several of the alternative choices for the production rate. Production Rate (R) Profit per Day (P) 0 $95 1 2 184 3 255 4 320 Because the profit goes up less than proportionally with the production rate (decreasing marginal returns), the management science team analyzing what this production rate (and the production rates of some other products) should be has decided to approximate the profit (P) by a simple nonlinear function of the production rate R. a. One such approximation is P = $100R- $5R2. How closely does this nonlinear function approximate the five values of P given in the table? b. Repeat part a for the approximation, P $104R- $6R2 c. Which of these two nonlinear functions provides the better fit to all the data? E* 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.

Answer 1

A.

A
P = 100*R - 5R^2	Error
0	0
95	0
180	4
255	0
320	0
Mean Error	0.8

B.

B
P = 104*R - 6*R^2	Error
0	0
98	3
184	0
258	3
320	0
Mean Error	1.2

C.

H14 F J K Production Rate Profit Per Day н B P = 104*R - 6*R^2 P = 100*R - 5R^2 Error Error 0 95 184 255 320 98 184 95 180 255 320 Mean Error 258 320 Mean Error Function A is providing a better fit to the given dataset because it have less mean error

D. y = -5.5714x2 + 102.29x - 0.3429

ཤཱ y= -5,5714x? + 102.29x - 0.3429 a 0. 51. 52535445