1). A canoe company manufactures two types of canoes: a two-person model and a four-person model. Each two-person model requires one hour in the cutting department and 1.5 hours in the assembly department. Each four-person model requires one hour in the cutting department and 2.75 hours in the assembly department. The cutting department has a maximum of 640 hours available per week and the assembly department has a maximum of 1080 hours available per week. The company earns a profit of $40 on each two-person canoe and a profit of $60 on each four-person canoe. How many canoes of each type should be manufactured each week in order to maximize profit? What is the maximum profit?
2) A furniture manufacturer makes two types of furniture – chairs and sofas. For simplicity, divide the production process into three distinct operations – carpentry, finishing, and upholstery. The amount of labor required for each operation varies. Manufacture of a chair requires 6 hours of carpentry, 1 hour of finishing and 2 hours of upholstery. Manufacture of a sofa requires 3 hours of carpentry, 1 hour of finishing, and 6 hours of upholstery. Due to limited availability of skilled labor as well as tools and equipment, the factory has available each day 96 labors – hours for carpentry, 18 labor- hours for finishing, and 72 labor hours for upholstery. The profit per chair is $80 and the profit per sofa $70. How many chairs and how many sofas should be produced each day to maximize the profit? What is the maximum profit?
3) An oil company has two refineries, one in Ohio and the other in Indiana. Each refinery can refine the amounts of fuel, in barrels, in a 24-hour period as shown in the table.
Maximum Production of:
Ohio
Indiana
Low-Octane gasoline
800
1000
High-Octane gasoline
500
600
Diesel
1000
600
Daily operating costs for the Ohio refinery are $28,000, and daily operating costs for the Indiana refinery are $33,000. The production manager of the oil company receives an order for 60,000 barrels of low-octane gasoline, 120,000 barrels of high-octane gasoline, and 150,000 barrels of diesel. How many days should the oil company operate each refinery to fulfill the order while minimizing operating costs? What is the minimum operating costs?
4) A farmer in California has 280 acres to grow asparagus, cauliflower, and celery. Asparagus requires 240 lb/acre of nitrogen, 148 lb/acre of phosphate, and 42 lb/acre of potash. Cauliflower requires 215 lb/acre of nitrogen, 98 lb/acre of phosphate, and 69 lb/acre of potash. Celery requires 336 lb/acre of nitrogen, 171 lb/acre of phosphate, and 147 lb/acre of potash. The farmer can get no more than 65,970 lb of nitrogen, 31,860 lb of phosphate, and 21,620 lb of potash. If he expects a profit of $160 per acre for asparagus, $90 per acre for cauliflower, and $80 per acre for celery, how many acres should he allot for each crop in order to maximize profit? What is the maximum profit that can be attained under these conditions?
Use the order calculator below and get started! Contact our live support team for any assistance or inquiry.
[order_calculator]