Transportation A manufacturer purchases a part for use at both of its plants—one at Roseville, California, the other at Akron, Ohio. The part is available in limited quantities from two suppliers. Each supplier has 75 units available. The Roseville plant needs 40 units, and the Akron plant requires 75 units. The first supplier charges $70 per unit delivered lo Roseville and $90 per unit delivered to Akron. Corresponding costs from the second supplier are $80 and $120. The manufacturer wants to order a total of 75 units from the first, less expensive supplier, with the remaining 40 units to come from the second supplier. If the company spends $10,750 to purchase the required number of units for the two plants, find the number of units that should be sent from each supplier to each plant.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Finite Mathematics (11th Edition)
- A custom-blend bird seed is made by mixing two types of bird seeds costing $0.75 per pound and $1.25 per pound. How many pounds of each type of seed mixture are used to make 200 pounds of custom-blend bird seed costing $0.95 per pound?arrow_forwardLast year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 8%, the Jeep by 5%, and the Toyota by 12%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year?arrow_forwardAt the Pizza Dude restaurant, a 12-in. pizza costs 5.40 to make, and the manager wants to make at least 4.80 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?arrow_forward
- A manufacturer purchases a part for use at both of its plants-one at Roseville, California, the other at Akron, Ohio. The part is available in limited quantities from two suppliers. Each supplier has 90 units available. The Roseville plant needs 50 units, and the Akron plant requires 90 units. The first supplier charges $70 per unit delivered to Roseville and $90 per unit delivered to Akron. Corresponding costs from the second supplier are $80 and $140. The manufacturer wants to order a total of 90 units from the first, less expensive supplier, with the remaining 50 units to come from the second supplier. If the company spends $14,100 to purchase the required number of units for the two plants, find the number of units that should be sent from each supplier to each plant. Write a linear system of equations. The number of units sent from the first supplier to Roseville is w, the number of units sent from the first supplier to Akron is x, the number of units sent from the second supplier…arrow_forwardA contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Hauling Cost per Ton at Site Pit 1 3 Price per Ton North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site. a. Formulate this problem as an assignment problem by constructing the appropriate cost table,…arrow_forwardA manufacturing company purchases two important parts from two different suppliers in the same region. The two suppliers are located about 100 miles apart. There are two shipping options for the two parts ordered. Option 1: Orders are shipped separately from each supplier. The contracted trucking company charges $720 for a shipment from each supplier. Option 2: Orders are aggregated in a single shipment. The trucking company needs to drive additional 100 miles to pick up orders from the other supplier. So there will be an additional charge of $283 for the additional stop. The weekly demand and unit cost information are listed in the table below (assume 52 weeks/year). Assume the unit annual holding cost is 16% of the unit cost for part A, and 18% for part B. Part A Part B Average weekly demand 400 513 Unit cost $39 $14 Please determine the average flow time (in weeks) in option 2. Numbers only. Keep 3-decimal if not exact, either round up or down is ok.arrow_forward
- A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 80 hrs of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.arrow_forwardA manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute for packing. Product B requires two minutes per unit for molding, four minutes for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have contributions of $1.50 per unit. a. Define decision variables for this problem. b. Define the objective function for this problem. c. Define constraints for this problem.arrow_forwardMrs. Doubtfire owns two properties in two different towns. House #1 has a market value of $243,569 and is assessed at 45% of its market value. The tax rate is $5.75 per $1000. House #2 has a market value of $179,087 and is assessed at 55% of its market value. The tax rate is 19.6 mills per $1. What is the total tax Mrs. Doubtfire will have to pay for both homes.arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell