In the assignment problem, the optimal solution is arrived when: a. Number of rows less than number of columns b. Number of columns less than number of rows c. Each row and column has only one zero d. Each row and column has at least one zero e. Number of lines = number of rows + 2* number of columns

To receive a grade of A, the average of four 100-point exams must be 90 or better. If a student received scores of 87, 84, and 95 on the first three exams, what minimum score does he need on the fourth exam to earn an A?

For each problem, show all work and explain your reasoning.(a) Does the overall configuration consider the order of the individual pieces of the configuration? (b) Count the number of different configurations for the prompt.1. Passwords of length seven containing distinct letters consisting of uppercase English lettersand/or lowercase English letters2. Committees consisting of four folks formed from the 11 Math faculty members3. Usernames of length six consisting of uppercase English letters, lowercase English letters,and/or numbers from 0–94. Election results from 6 Math 150 students for course president, vice president, and treasurer5. Phone numbers containing only odd numbers6. Social security numbers containing neither 8’s nor 9’s7. Ice cream sundaes consisting of three distinct flavors taken from ten total flavors8. Handfuls of five Skittles consisting of only “warm” colors from a jar containing 8 red, 11green, 7 yellow, 12 purple, and 13 orange9. Possible rolls from fair 6-sided,…

A farmer has 165 acres of land suitable for cultivating crops A and B. He has enough seeds available to plant 110 acres of crop A and 115 acres of crop B. Each acre of crop A requires 18 hours of labor, and each acre of crop B requires 19 hours of labor. The farmer has at most 3420 hours of labor available. He expects to make a profit of 130 dollars per acre on crop A and 190 dollars per acre on crop B. How many acres should the farmer plant in order to maximize his profit? acres of crop A, and acres of crop B.