Question

Assume that a competitive firm has the total cost function: TC=1q3−40q2+720q+2000

Suppose the price of the firm's output (sold in integer units) is $700 per unit.

Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level? Please specify your answer as an integer.

Answer 1

Since you have asked for not using calculus but only table, here i have constructed the following table:

Price	Quantity	Revenue	Total Cost	Profit
700	1	700	2681	-1981
700	2	1400	3288	-1888
700	3	2100	3827	-1727
700	4	2800	4304	-1504
700	5	3500	4725	-1225
700	6	4200	5096	-896
700	7	4900	5423	-523
700	8	5600	5712	-112
700	9	6300	5969	331
700	10	7000	6200	800
700	11	7700	6411	1289
700	12	8400	6608	1792
700	13	9100	6797	2303
700	14	9800	6984	2816
700	15	10500	7175	3325
700	16	11200	7376	3824
700	17	11900	7593	4307
700	18	12600	7832	4768
700	19	13300	8099	5201
700	20	14000	8400	5600
700	21	14700	8741	5959
700	22	15400	9128	6272
700	23	16100	9567	6533
700	24	16800	10064	6736
700	25	17500	10625	6875
700	26	18200	11256	6944
700	27	18900	11963	6937
700	28	19600	12752	6848
700	29	20300	13629	6671
700	30	21000	14600	6400
700	31	21700	15671	6029
700	32	22400	16848	5552
700	33	23100	18137	4963
700	34	23800	19544	4256
700	35	24500	21075	3425
700	36	25200	22736	2464
700	37	25900	24533	1367
700	38	26600	26472	128
700	39	27300	28559	-1259
700	40	28000	30800	-2800
700	41	28700	33201	-4501
700	42	29400	35768	-6368
700	43	30100	38507	-8407
700	44	30800	41424	-10624
700	45	31500	44525	-13025

Total Revenue = Price * Quantity

Profit = Total Revenue - Total Cost

We can see that the Profit is maximized at units 26

Let us verify this using calculus

Equating it to zero

Hence, the firm will produce 26 units