|
Question 86577: 7.3
5. A farmer has 90 acres available for planting millet and alfalfa. Seed costs $4 per acre for millet and $6 per acre for alfalfa. Labor costs are $20 per acre for millet and $10 per acre for alfalfa. The expected income is $110 per acre for millet and $150 per acre for alfalfa. The farmer intends to spend no more than $480 for seed and $1400 for labor.
a. Write a system of linear inequalities to represent the constraints.
b. Graph the feasible region
c. Write the objective function that maximizes the income, and find the
maximum income for the given constraints.
6. The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can product, at most, 200 units of paper a day. At least 10 units of notebook paper and 80 units of newsprint are required daily by regular customers. The profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350.
a. Write a system of linear inequalities to represent the constraints.
b. Graph the feasible region.
c. Write the objective function that maximizes the income, and find the
maximum income for the given constraints.
6. Jerry works no more than 20 hours a week during the school year. He is paid $10 an hour for tutoring geometry students and $7 an hour for delivering pizzas for Pizza King. He wants to spend at least 3 hours, but no more than 8 hours, a week tutoring. Find Jerry’s maximum weekly earnings.
7. A theater where a drug abuse program is being presented seats 150 people. The proceeds will be donated to a local drug information center. Admission is $2.00 for adults and $1.00 for students. Every two adults must bring at least one student. How many adults and students should attend in order to raise the maximum amount of money?
8. The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space and a bus requires 30 square meters of space. The attendant can handle no more than 60 vehicles.
a. Let c be the number of cars and let b be the number of buses. Write a system of inequalities to represent the amount of space available and the total number of vehicles allowed.
b. If a car is charged $2.50 to park and a bus is charged $7.50, how many of each should the attendant accept to maximize income?
c. The parking lot prices for special events are $4.00 for cars and $8.00 for buses. How many of each vehicle should the attendant accept during a special event?
7.4
1. A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color B requires 1 unit of yellow dye and 6 units of green dye. Find the constraints, graph the feasible region, and find the maximum number of gallons possible.
2. A delicatessen has 10 pounds of garlic-flavored sausage and 10 pounds of plain sausage. The deli wants to make as many pounds of bratwurst as possible. Each pound of bratwurst requires ˝ pound of garlic-flavored sausage and ˝ pound of plain sausage. Find the maximum number of pounds of bratwurst that can be made.
3. Machine A can produce 30 steering wheels per hour at a cost of $16 per hour. Machine B can produce 40 steering wheels per hour at a cost of $22 per hour. At least 360 steering wheels must be made in each 8-hour shift. What is the least cost involved in making 360 steering wheels, if maintenance of the machines limits their use to no more than 8 consecutive hours?
4. The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each should be accepted to maximize income?
5. The cost to run Machine 1 for an hour is $2. During that hour, Machine 1 produces 240 bolts and 100 nuts. The cost to run Machine 2 for an hour is $2.40. During that hour, Machine 2 produces 160 bolts and 160 nuts. With a combined running time of no more than 30 hours, how long should each machine run to produce an order of at least 2080 bolts and 1520 nuts at the minimum operating cost?
6. The Oklahoma City division of SuperSport, Inc produces footballs and basketballs. It takes 4 hours on machine A and 2 hours on machine B to make a football. Producing a basketball requires 6 hours on machine A, 5 hours on machine B and 1 hour on machine C. Machine A is available 120 hours a week, machine B is available 72 hours a week, and machine C is available 10 hours per week. If the company makes $3 profit on each football and $2 profit on each basketball, how many of each should they make to maximize their profit?
Answer by Flake(45)   (Show Source):
|
|
|
| |
