As a member of Analysts Incorporated consulting firm, you have carefully collected data on a manufacturing firm's output, capital and labor. The data are in the spreadsheet below. You believe the firm's production function to be Cobb-Douglas, Q = CK^aL^b.

a. Use regression analysis to get estimates for the parameters a and b from the Cobb-Douglas production function. Round your answers to the nearest hundredth.

Estimate for a:

Estimate for b:

b. Suppose capital is fixed at 400 and the price of output is $100. If labor costs $95per unit, how many units of labor should the firm hire to maximize profits? Round your answer to the nearest whole number.

c. If labor costs $75 per unit and capital costs $125 per unit, what is the cost-minimizing input mix for producing 4,000 units of output? Round your answers to the nearest whole number.

Labor:

Capital:

Spreadsheet Data

Output	Capital	Labor
3563	374	213
4554	360	285
3658	379	213
4107	361	231
3639	438	204
2610	368	216
5497	432	244
4219	400	245
4400	420	231
3812	455	255
4817	370	270
3762	384	206
5579	492	262
5834	374	235
5365	426	264
5153	437	271
4843	436	218
4752	474	274
5492	490	283
4654	404	310
5256	451	262
2960	382	235
7416	498	302
4727	391	233
6702	461	275
5059	377	231
4914	459	298
8769	448	295
3313	412	210
5164	445	235
4925	487	212
4781	447	228
5716	381	272
6983	394	261
5723	446	279
5441	359	207
3446	353	289
3588	401	218
5196	354	255
5171	380	284
4661	482	210
4967	485	284
4122	397	309
4603	438	267
4538	399	219
4615	393	248
4877	401	241
6627	413	267
4035	359	248
4445	424	234
6224	443	294
5384	460	279
5406	416	266
5104	422	307
4990	370	203
4478	493	237
4917	365	302
4735	457	252
2877	432	236
4898	425	274
8642	483	232
5758	438	281
4139	405	202
3559	479	217
3492	438	244
5089	397	216
5177	384	229
5886	395	296
5874	397	297
3760	448	243
5728	373	305
5684	482	247
2825	436	252
5709	411	226
5325	389	306
5325	494	252
3566	416	291
4158	413	263
4226	431	244
5652	424	284
4737	399	204
4401	369	280
6437	466	281
4362	382	288
5779	376	283
4684	371	248
5201	499	201
3508	362	289
4858	356	221
4084	387	237
5197	499	270
5052	464	262
6069	469	304
5492	354	290
3609	420	258
5378	460	239
4863	416	222
6067	398	273
5279	419	286
5037	424	206
6067	430	286
4222	449	309
4967	481	206
5745	385	276
5552	479	284
5324	387	291
4997	356	310
5908	470	302
6020	373	220
4860	433	218
6891	463	292
4874	483	235
4941	394	293
4255	380	258
5564	495	268
8218	410	303
3825	357	263
5508	431	249
3001	391	211
4709	361	283
4547	471	205
3364	486	227
6610	453	266
5345	440	310
4167	363	211
4040	350	310
5265	488	254
5307	449	271
4033	387	244
7577	387	249
4229	473	235
3896	366	240
4959	405	223
4624	367	304
5793	398	269
6634	448	295
3950	360	206
6634	486	225
5629	427	298
5406	446	242
5209	454	290
5536	469	272
4885	499	310
3959	498	226
5414	382	232
5634	380	231
6682	454	284
3935	445	304
4936	440	257
3855	466	230
5417	411	233
5318	467	265
4173	474	237
4200	416	281
5726	477	288
5009	415	213
5914	450	265
4771	439	243
7434	438	248
3903	379	219
3656	428	264
4219	368	243
4241	483	231
7098	376	242
7518	441	282
4456	366	208
3615	363	218
6359	380	231
5295	353	242
6205	437	271
5667	431	298
5760	458	252
4506	385	222
4334	452	283
5363	467	268
5328	384	292
5115	354	261
6509	453	264
5037	455	212
4587	387	295
4801	472	227
4862	376	261
3375	397	251
6037	461	281
5910	375	295
4485	467	256
5417	408	260
3558	458	232
3573	352	247
4758	469	277
5950	373	207
6012	442	292
4960	403	272
5794	449	209
5805	403	291
4443	377	227
4367	362	217
4659	352	275
3944	438	289
4596	470	289
4775	385	225
7635	462	243
8054	483	201