Consider a firm selling their product at price p=70. The firm needs to hire a seller; the seller disutility from exerting effort to sell and the firms production cost are summarized in the following spreadsheet.

Question:

Suppose that the firm design the seller's pay as the sum of a fixed salary component "a" and a bonus "b" for each unit sold (a linear incentive scheme). What is the linear bonus "b" that maximizes the firm's profits?

Number of Units Sold	Effort Disutility (Total)	Production Cost (Total)
0	20	0
1	20.5	25.5
2	22	51
3	24.5	76.5
4	28	102
5	32.5	127.5
6	38	153
7	44.5	178.5
8	52	204
9	60.5	229.5
10	70	255
11	80.5	280.5
12	92	306
13	104.5	331.5
14	118	357
15	132.5	382.5
16	148	408
17	164.5	433.5
18	182	459
19	200.5	484.5
20	220	510
21	240.5	535.5
22	262	561
23	284.5	586.5
24	308	612
25	332.5	637.5
26	358	663
27	384.5	688.5
28	412	714
29	440.5	739.5
30	470	765
31	500.5	790.5
32	532	816
33	564.5	841.5
34	598	867
35	632.5	892.5
36	668	918
37	704.5	943.5
38	742	969
39	780.5	994.5
40	820	1020
41	860.5	1045.5
42	902	1071
43	944.5	1096.5
44	988	1122
45	1032.5	1147.5
46	1078	1173
47	1124.5	1198.5
48	1172	1224
49	1220.5	1249.5
50	1270	1275
51	1320.5	1300.5
52	1372	1326
53	1424.5	1351.5