(X, = -2, x, = 4, ɛ, = 15 (x1 = 1.75, x, = 2, x3 :

8) Employ the following methods to find the maximum of f(x)= 4x–1.8x²+1.2x - 0.3x (a) Golden-section search (x; = -2, x, = 4, ɛ; = 1%). (b)Parabolic interpolation (xo = 1.75, x1 = 2, x2 = 2.5, iterations = 4). Select new points sequentially as in the secant method. (c) Newton's method (xo = 3, ɛ; = 1%).

b) Data was collected on 344 corporate executives to find out the effect of MBA degree and work experience on their salary. The following model was estimated: Y = 2.3501 + 3.6306D11 – 2.6354 D2i + 0.8527 X¡ + 1.634 (D, * X)i (2.1805) (- 3.457) (1.263) (7.605) (2.98) R? = 0.8968 Y: Annual Income in Lakhs of Rupees Di and D2 are MBA and gender dummies respectively X: Work experience in years DI = 1 if one has MBA degree = 0 otherwise D2 = 1 for a female executive = 0 for a male executive i. Write the regression equations for female MBA executives and male MBA executives separately. ii. Find the mean income level for the reference category and interpret it. iii. Test the statistical significance of differential intercept coefficient between female MBA executives and Male MBA executives at 5% level of significance. iv. Interpret the coefficient of D,*Xi.

Denote owl and wood rat populations in a particular area at time k by xk LK Rk where k is the time in months, Lk is the number of owls in the area studied, and R is the number (in thousands) of wood rats in the area studied. Suppose Lk+ 1 = (0.2)Lk + (0.6)Rk and Rk+1=(-0.1)Lk + (0.9)Rk. Determine the evolution of this system. (Give a formula for xk.) Does the owl population grow or decline? Does the wood rat population grow or decline?

2) Employ the following methods to find the maximum of f(x) = 4x –1.8x2 +1.2x³ – 0.3x* (a) Golden-section search (x; = -2, xụ = 4, ɛ; = 1%). (b)Parabolic interpolation (xo = 1.75, x1 = 2, x2 = 2.5, iterations = 4). Select new points sequentially as in the secant method. (c) Newton's method (xo = 3, ɛ: = 1%).

Suppose that 40 deer are introduced in a protected area. The population of the herd P can be modeled by P = 40 + 20x / 1 + .05x  where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.

Chapter 4, Section 4.2, Question 014 Use the first derivative to find all critical points and use the second derivative to find all inflection points. Use a graph to identify each critical point as a local maximum, a local minimum, or neither. f (x) = 2x + 3x² – 180x + 6 Enter the exact answers in increasing order. If there is no answer, enter "NA". The critical point at x = is The critical point at x = is The inflection point is x = Click if you would like to Show Work for this question: Open Show Work

Please let me know how to find out the answer for (b) using the substitution method. I know how to get the functions for (2) as shown.  Question:  A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a) Formulate this as a linear…

An advertising firm is hired to promote a new television show for 3 weeks before its debut and 2 weeks afterward. After t weeks of advertisement campaign, it is found that P(t) percent of the viewing public is aware of the show, where P(t) = (59t/0.7t^2+16) + 6 a. What is the average percentage of the viewing public is aware of the show during the 5 weeks of advertising campaign? (Hint: P(0) is already in the unit of percent) b. At what time during the first 5 weeks of the campaign is the percentage of viewers is the same as the average percentage found in part (a)? (Hint: use algebra or graph to solve the problem

The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores.  Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product.  Let X = miles that the tires last:   X~N(60,000  2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free.  Assume the distribution of tire mileage is normal.