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Example 4.2. In the ampli er of Fig. 4-5(a), VDD 20 V; R1 1 M ; R2 15:7 M ; RD 3 k , and RS 2 k . If the JFET characteristics are given by Fig. 4-6, nd (a) IDQ , (b) VGSQ , and (c) VDSQ . (a) By (4.3), VGG R1 1 106 VDD 20 1:2 V R1 R2 16:7 106

On Fig. 4-6(a), we construct the transfer bias line (4.4); it intersects the transfer characteristic at the Q point, giving IDQ 1:5 mA. (b) The Q point of Fig. 4-6(a) also gives VGSQ 2 V. (c) We construct the dc load line on the drain characteristics, making use of the vDS intercept of VDD 20 V and the iD intercept of VDD = RS RD 4 mA. The Q point was established at IDQ 1:5 mA in part a and at VGSQ 2 V in part b; its abscissa is VDSQ 12:5 V. Analytically, VDSQ VDD RS RD IDQ 20 5 103 1:5 10 3 12:5 V

Accounting for the corporation is distinguished from accounting for the sole proprietorship or the partnership by the treatment of owner s (stockholder s) equity, which, in the corporation, is separated into paid-in cap ital and retained earnings. The reason for this separation is that most states prohibit corporations from paying dividends from other than retained earnings. Paid-in capital is further divided, and so we have three major capital accounts: 1. Capital Stock. This account shows the par value of the stock is sued by the corporation. 2. Additional Paid-in Capital. Amounts paid in beyond the par val ue of stock. 3. Retained Earnings. The accumulated earnings arising from prof itable operation of the business.

Fig. 14-2

CHAP. 4]

1 2000

Fig. 14-3

1 1.2

VGSQ (a)

14.5 A manufacturer sells each of his TV sets for $85. The cost C (in dollars) of manufacturing and selling x TV sets per week is C = 1500 + 10x + 0.005x 2 If at most 10 000 sets can be produced per week, how many sets should be made and sold to maximize the weekly pro t

gs ,

If a corporation issues only one class of stock, it is known as common stock, with all shares having the same rights. The ownership of a share of common stock carries with it the right to: 1. Vote in the election of directors and in the making of certain im portant corporate decisions. 2. Participate in the corporation s pro ts. 3. Purchase a proportionate part of future stock issues. 4. Share in assets upon liquidation.

_ 1. 0

For x sets per week, the total income is 85x. The pro t is the income minus the cost, P = 85x (1500 + 10x + 0.005x 2 ) = 75x 1500 0.005x 2 We wish to maximize P on the interval [0, 10 000], since the output is at most 10 000. dP = 75 0.01x dx and the critical number is the solution of 75 0.01x = 0 0.01x = 75 75 x= = 7500 0.01 We now construct Table 14-5 (see below): P(7500) = 75(7500) 1500 0.005(7500)2 = 562 500 1500 0.005(56 250 000) = 561 000 281 250 = 279 750 P(0) = 75(0) 1500 0.005(0)2 = 1500 P(10 000) = 75(10 000) 1500 0.005(10 000)2 = 750 000 1500 0.005(100 000 000) = 748 500 500 000 = 248 500 Thus, the maximum pro t is achieved when 7500 TV sets are produced and sold per week. Table 14-5 x 7500 0 10 000 P(x) 279 750 1500 248 500

a _2 Q b _3 _4

20 25

0 1 _ 1.1 0 5 10

14.6 An orchard has an average yield of 25 bushels per tree when there are at most 40 trees per acre. When there are more than 40 trees per acre, the average yield decreases by 1 bushel per tree for every tree over 40. Find the 2 number of trees per acre that will give the greatest yield per acre.

_ 5.2