1 .		Find the coordinates of the corner points of the solution region for:
2 .		The corner points for the bounded feasible region determined by the system of inequalities: are O = (0, 0), A = (0, 7), B = (6, 5) and C = (8, 0). Find the optimal solution for the objective profit function: maximize P = 5x + 5y.
3 .		A vineyard produces two special wines a white, and a red. A bottle of the white wine requires 14 pounds of grapes and 1 hour of processing time. A bottle of red wine requires 25 pounds of grapes and 2 hours of processing time. The vineyard has on hand 2,198 pounds of grapes and can allot 160 hours of processing time to the production of these wines. A bottle of the white wine sells for $11.00, while a bottle of the red wine sells for $20.00. How many bottles of each type should the vineyard produce in order to maximize gross sales?
4 .		Formulate the following problem as a linear programming problem (DO NOT SOLVE): A dietitian can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.02. Each ounce of chicken contains 13 units of protein and 24 units of carbohydrates. Each ounce of potatoes contains 5 units of protein and 35 units of carbohydrates. The minimum daily requirements for the patients under the dietitian's care are 45 units of protein and 58 units of carbohydrates. How many ounces of each type of food should the dietitian purchase for each patient so as to minimize costs and at the same time insure the minimum daily requirements of protein and carbohydrates? (Let x equal the number of ounces of chicken and y the number of ounces of potatoes purchased per patient.)
5 .		A small accounting firm prepares tax returns for two types of customers: individuals and small businesses. Data is collected during an interview. A computer system is used to produce the tax return. It takes 2.5 hours to enter data into the computer for an individual tax return and 3 hours to enter data for a small business tax return. There is a maximum of 40 hours per week for data entry. It takes 20 minutes for the computer to process an individual tax return and 30 minutes to process a small business tax return. The computer is available for a maximum of 900 minutes per week. The accounting firm makes a profit of $100 on each individual tax return processed and a profit of $175 on each small business tax return processed. How many of each type of tax return should the firm schedule each week in order to maximize its profit? (Let x equal the number of individual tax returns and y the number of small business tax returns.)
6 .		Formulate the following problem as a linear programming problem (DO NOT SOLVE): A steel company produces two types of machine dies, part A and part B. Part A requires 6 hours of casting time and 4 hours of firing time. Part B requires 8 hours of casting time and 3 hours of firing time. The maximum number of hours per week available for casting and firing are 85 and 70, respectively. The company makes a $2.00 profit on each part A that it produces, and a $6.00 profit on each part B that it produces. How many of each type should the company produce each week in order to maximize its profit? (Let x equal the number of A parts and y equal the number of B parts produced each week.)
7 .		Consider the following linear programming problem. A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% Jamaican and sells for $3 a pound. Each pound of blend B contains 35% Mocha Java and 65% Jamaican and sells for $2.25 a pound. The merchant has available 1000 pounds of Mocha Java and 600 pounds of Jamaican. The merchant will try to sell the amount of each blend that maximizes her income. Let x be the number of pounds of blend A and y be the number of pounds of blend B. The objective function is:
8 .		Consider the following linear programming problem. A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% Jamaican and sells for $3 a pound. Each pound of blend B contains 35% Mocha Java and 65% Jamaican and sells for $2.25 a pound. The merchant has available 1000 pounds of Mocha Java and 600 pounds of Jamaican. The merchant will try to sell the amount of each blend that maximizes her income. Let x be the number of pounds of blend A and y be the number of pounds of blend B. One inequality which must be satisfied is:
9 .		A business entrepreneur sells two mixtures of nuts. Each pound mixture A contains 70% cashews and 30% walnuts and sells for $3 a pound. Each pound of mixture B contains 45% cashews and 55% walnuts and sells for $2.75 a pound. The entrepreneur has available 900 pounds of cashews and 500 pounds of walnuts. The entrepreneur will try to sell the amount of each mixture that maximizes income. Let x be the number of pounds of mixture A and y be the number of pounds of mixture B. The objective function is:
10 .		A small company produces three kinds of guitars, traditional, electric and bass, in two factories. Factory A produces 8 traditional, 5 electric and 10 bass guitars in one day, while factory B produces 7 traditional, 9 electric and 8 bass guitars in one day. An order is received for 10 traditional, 15 electric and 18 bass guitars. It costs $900 a day to operate factory A and $1000 a day to operate factory B. The manufacturer chooses the number of days to operate each factory in order to minimize cost. The objective function is:
11 .		A small company produces three kinds of guitars, traditional, electric and bass, in two factories. Factory A produces 8 traditional, 5 electric and 10 bass guitars in one day, while factory B produces 7 traditional, 9 electric and 8 bass guitars in one day. An order is received for 10 traditional, 15 electric and 28 bass guitars. It costs $900 a day to operate factory A and $1000 a day to operate factory B. The manufacturer chooses the number of days to operate each factory in order to minimize cost. Which of the following inequalities must be satisfied?
12 .		Consider the feasible set (FS) consisting of the following points: (2,5), (4,5), (2,3), (3,2),(4,2) The maximum value of the objective function is
13 .		Consider the feasible set: and and . Which of the following is not in the feasible set?
14 .		New trucks are transported from docks in Portland and Providence to dealerships in Raleigh and Rollestown. The dealership in Raleigh needs 20 trucks and the dealership in Rollestown needs 15 trucks. It costs $60 to transport a truck from Portland to Raleigh, $45 to transport a truck from Portland more to Philadelphia, $65 to transport a truck from Providence to Raleigh, and $40 to transport a truck from Providence to Rollestown. There are 30 trucks on the docks in Portland and there are 18 trucks on the docks in Providence. The number of trucks sent from each dock to each dealership is chosen to minimize total transportation costs. If x represents the number of trucks sent from Portland to Rollestown and y represents the number of trucks sent from Providence to Raleigh, then the number of trucks sent from Portland to Raleigh is given by:
15 .		There is exactly $20,000 in a trust fund which is to be invested among three types of bonds, A, B, and C, which yield 4%, 5% and 6%, respectively, on the investment. The total yield must be at least $500, no less than $2000 may be invested in B bonds, and no more than $3000 may be invested in A bonds. If x and y represent the amounts invested in A and B bonds, then the amount invested in C bonds is:
16 .		Consider the feasible set defined by the points (0,7), (1,5), (5,1), (7,0) Find an objective function of the form which has its least value at the point (5,1).
17 .		Consider the feasible set bounded by the points: A: (0,5) B: (3,4) C: (4,3) D: (5,0) O: (0,0). The point where the objective function is a maximum is
Answer choices in this exercise are randomized and will appear in a different order each time the page is loaded.