The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to: 2 X1 + 5 X2 ≤ 200 3 X1 + 7 X2 ≤ 175 X1, X2 ≥ 0 How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Design a number line containing five (5) points2.benin, one of the smallest countries in africa, has a total area of 43,475 square miles. the population of the country was recently estimated at 10,160,555. about 3,657,790 people live in rural areas. the country has only about 870 miles of surfaced roads. a. round off the total population to the nearest hundred thousand people. b. round off benin’s area in square miles to the nearest thousand. c. round off the number of miles of surfaced roads to the nearest ten. d. round off the number of people who live in rural areas to the nearest million.

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Find the distance from the theater to the library. leave your answer in simplest radical form if necessary. 12 √12 74 √74