An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. he has $50,000 to invest. because of the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%. assuming that investment returns are as expected, how much should be invested in each in order to maximize his return?

let o = the amount invested in oil leases,
let s = the amount invested in stocks, and
let b = the amount invested in bonds

which option (a, b, c, or d) shows the correct objective function and constraints for this application?

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b = 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 9%*o + 5%*s + 15%*b
constraints: o + s + b = 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b < 50,000, o + s < = 30%*50,000, o + b < = 50%*50,000, o > = 0, s > = 0, b < = 0

objective function: maximize return, r = 15%*o + 9%*s + 5%*b
constraints: o + s + b < 50,000, o + s > = 30%*50,000, o + b > = 50%*50,000, o > = 0, s > = 0, b < = 0

Question 5 spring semester final exam math evaluate

If sec theta = 5/3 and the terminal point determined by theta is in quadrant 4, then

(c) compare the results of parts (a) and (b). in general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c. there is no distinct pattern when each data value is multiplied by the same constant. (d) suppose you have information about average heights of a random sample of airline passengers. the mode is 65 inches, the median is 72 inches, and the mean is 65 inches. to convert the data into centimeters, multiply each data value by 2.54. what are the values of the mode, median, and mean in centimeters? (enter your answers to two decimal places.) mode cm median cm mean cm in this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. consider the following data set 7, 7, 8, 11, 15. (a) compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = (b) multiply 3 to each of the data values. compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = --