Fill in the top 8 matrixes (not the 9th) in the Matrices below, easily by copying them into an Excel File, using the proper formula in each cell. Keep all the digits as you do the calculations and move through the tables. *Identify the profit-maximizing cell in each matrix by shading it any color in all of the nine matrices.

	1. DETERMINE OUTPUT (Q)		5. CALCULATE REVENUE FROM SALES (PQ)
	A	2	Q =AKL	LABOR USED				PQ	LABOR USED
		0.67	1	2	3	4	5	6				1	2	3	4	5	6
		0.25	CAPITAL USED	1									CAPITAL USED	1
	P	310	2								2
	W	140	3				5.883366				3
	R	360	4								4
	=2/3. =1/4. +=11/12=RTS	5								5
	6								6
	2. FIND TOTAL FACTOR COSTS		6. DETERMINE PROFIT
			WL + RK	LABOR USED				PQ - (WL + RK)	LABOR USED
			1	2	3	4	5	6				1	2	3	4	5	6
		CAPITAL USED	1									CAPITAL USED	1
	2								2
	3								3
	4								4
	5								5
	6								6
	3. CALCULATE LABOR'S MARGINAL PRODUCT		7. CALCULATE CAPITAL'S MARGINAL PRODUCT
			MPL	LABOR USED				MPK	LABOR USED
			1	2	3	4	5	6				1	2	3	4	5	6
		CAPITAL USED	1									CAPITAL USED	1
	2								2
	3								3
	4								4
	5								5
	6								6
	4. CALCULATE THE VALUE OF LABOR'S MARGINAL PRODUCT		8. CALCULATE THE VALUE OF CAPITAL'S MARGINAL PRODUCT
			PMPL	LABOR USED				PMPK	LABOR USED
			1	2	3	4	5	6				1	2	3	4	5	6
		CAPITAL USED	1									CAPITAL USED	1
	2								2
	3								3
	4								4
	5								5
	6								6
	9. CALCULATE THE MARGINAL COST OF PRODUCTION
			MC	LABOR USED			The tables here only show the values of output, cost, revenue, etc. commensurate with hiring whole units of capital and labor. In practice, the time period during which production occurs can be set such that any values of K, L, Q, C, etc. are possible. Solving for the exact Q*, L*, K*, etc. is a straightforward mathematical optimization (calculus) exerise and I am happy to provide you these equations upon request.
			1	2	3	4	5	6
		CAPITAL USED	1	0.00	0.00	0.00	0.00	0.00	0.00
	2	0.00	0.00	0.00	0.00	0.00	0.00
	3	0.00	0.00	0.00	300.80	0.00	0.00
	4	0.00	0.00	0.00	0.00	0.00	0.00
	5	0.00	0.00	0.00	0.00	0.00	0.00
	6	0.00	0.00	0.00	0.00	0.00	0.00