Mick garcia, a certified financial planner (cfp), has been asked by a client to invest $250,000. this money may be placed in stocks, bonds, or a mutual fund in real estate. the expected return on investment is 13% for stocks, 8% for bonds, and 10% for real estate. while the client would like a very high expected return, she would be satisfied with a 10% expected return on her money. due to risk considerations, several goals have been established to keep the risk at an acceptable level. one goal is to put at least 30% of the money in bonds. another goal is that the amount of money in real estate should not exceed 50% of the money invested in stocks and bonds combined. in addition to these goals, there is one absolute restriction. under no circumstances should more than $150,000 be invested in any one area.
formulate this as a goal programming problem. assume that all of the goals are equally important.
use any available software to solve this problem. how much money should be put in each of the investment options? what is the total return? which of the goals are not met?

Mary used 1/7 of a spool of ribbon to complete 4 projects. she used the same amount of ribbon on each project. how much ribbon did she use on each project?

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

Find the solution of each of the following.