Question

Your hospital has a demand function given by P = 404 - 2Q where P is the price of hospital care and Q is the quantity of hospital care. The marginal revenue (MR) function is given by MR = 404 – 4Q. The total cost function (TC) is given by TC = 300 + 4Q + 8Q² and the marginal cost (MC) is given by MC = 4 + 16Q.

1. Find the total revenue (TR) function which is a function of quantity (Q) and show your work.

2. Fill in the blanks, A, B, C and D and show your work to find your answers.

P	Q	TR	TC	AC	MC	Profit
404	0	0	300			-300
394	5	1970	520	104	44	1450
	10			C
374	A				D
364	20	B	3580	179	284
354	25	8850	5400	216		E
344	30	10320	7620	254

3. Find the output that maximizes total revenue and show your work

4. Find the output that maximizes profit and show your work

5. Consider the four new management tools that have been introduced during the past four decades: benchmarking, total quality management, reengineering and the learning organization. Which tool includes Six Sigma aims to improve the process performance and achieve high levels of quality by investigating and eliminating causes of defects and minimizing process and product variability.

Answer 1

A.

P = 404-2Q --------- (1)

Multiply above equation by Q

P*Q = 404Q - 2Q^2

Or

TR = 404Q - 2Q^2

B.

P	Q	TR	TC	AC	MC	Profit
404	0	0	300			-300
394	5	1970	520	104	44	1450
384	10	3840	1140	114	124	2700
374	15	5610	2160	144	204	3450
364	20	7280	3580	179	284	3700
354	25	8850	5400	216	364	3450
344	30	10320	7620	254	444	2700

C.

Revenue is maximized, when output = 30

At this level, TR = 10320

D.

Profit is maximized, when output = 20  

At this level, profit = 3700 that is maximum among all the output level.

Pl. repost other unanswered questions for their proper answers!