Suppose that maggie cares only about chai and bagels. her utility function is u = cb, where c is goolsbee2e_ch04_appendix. indd 153 30/07/15 12: 36 pm 154 part 2 consumption and production the number of cups of chai she drinks in a day, and b is the number of bagels she eats in a day. the price of chai is $3, and the price of bagels is $1.50. maggie has $6 to spend per day on chai and bagels. a. what is maggie’s objective function? b. what is maggie’s constraint? c. write a statement of maggie’s constrained optimization problem. d. solve maggie’s constrained optimization problem using a lagrangian

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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