SolutionstoProjectCopy.docVIP

HE LING . . . . . . 2. convexity 3a. b. c. d. 4. a. b. j/1.963855.1541458.7595.000336.9635192.963519.000060458.13336 0.963519 5. a. | | | | | Betty 0 9 18 27 36 time(months) This is an annuity so we analyze as per b 6a. . Now So they must wait 15 years. b. c. i.01.025.05.06.08.1.15.2T463.82149.3961.21348.2832.81824.1613.5748.8275 7. Cash flow: 51- 2(8)- 1(3) = 51-19 = 32 (outflow) Y = W-32 X3035404550556065 0 0 0 0 5101520201510 5 0 0 0 0W1020304040353025Y-22-12-2 8 8 3-2-7 Lower Break Even Upper Break Even 8.a. K0K505050K150K=10172.61 positive0K=100-65.52 negativeincreasingab maxdecreasing So K = 50, L = is maximum 8 b. We solve this problem using Lagrange Multiplier We must solve that is  So 100(6K)+300K-45000 = 0 900K = 45000 K = 50 L = 300 Now P(50,300) = 8251.57 To show this is an absolute maximum we can use the Second Derivative Test for functions of 2 variables 9a. . So (logarithmic differentiation). no roots. . . maxima and minima table. xx = .1 x 1/e 1/e = .3679x =1 1/e xg(x)-1.035 negative 01 positiveg decreasingminima increasingis min