Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes $500. Formulate an LP that will maximize Truckco’s profit. Solve the problem using the simplex algorithm.

A bicycle manufacturer makes mountain bikes and road bikes. Each mountain bike requires 2 units of steel and 6 units of aluminum in its frame and 12 special components for the hub, sprocket, and gear assembly. Each road bike requires 5 units each of steel and aluminum for its frame and 5 of the special components. Shipments are such that steel is limited to 114 units per day, aluminum is limited to 142 units per day, and the special components are limited to 214 units per day. If the profits are $500 on each mountain bike and $400 on each road bike, how many of each should be produced to yield the maximum profit?

For a given week, Debra's Coffee House has available 1728 ounces of A grade coffee and 1760 ounces of B grade coffee. These are blended into 1-pound packages as follows: an economy blend that contains 2 ounces of A grade coffee and 10 ounces of B grade coffee, and a superior blend that contains 9 ounces of A grade coffee and 2 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package sold and a $4 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of each blend should it make to maximize its profit for the week?

The town councils of Cambridge, Bridgwater and Bath each placed an order with a tree nursery. Cambridge ordered 4 lime trees, 20 plane trees and 12 rowan trees, and the total cost was £1296. Bridgwater ordered 10 lime trees, 6 plane trees and 32 rowan trees, and the total cost was £1746. Bath ordered 8 lime trees, 14 plane trees and 16 rowan trees, and the total cost was £1498.By modelling the problem as a system of three linear simultaneousequations, use matrices to find the cost per tree of each type of tree.

A clothing manufacturer makes trousers,skirts and blouses.Each trouser requires 20 minutes of cutting time,60 minutes of sewing time and 5 minutes of packaging time.Each skirt requires 15 minutes of cutting time,30 minutes of sewing time and 12 minutes of packaging time.Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting,sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Inverse Method or the Cramers Rule, determine how many of each type of clothing should be made to use all available labour hours?

A transport company has two types of trucks, Type A and Type B. Type A has a refrigerated capacity of 20m and a non-refrigerated capacity of 40m while Type B has the same overall volume with equal sections for refrigerated and non-refrigerated stock. A grocer needs to hire trucks for the transport of 3,000m of refrigerated stock and 4,000m of non-refrigerated stock. The cost per kilometer of a Type A is $30, and $40 for Type B. How many trucks of each type should the grocer rent to achieve the minimum total cost? * Suppose x=type A trucks, y=type B trucks, write the objective function.

Hello Dolly, Inc. crafts three styles of dolls: Lexi, Maysy, and Dizzy. Each doll requires sewing time, painting time, and supplies. Sewing machines are available for only 118 hours, only 2805 hours are available for painting, and 390.5 lbs. of supplies are available. Each Lexi doll requires 0.2 hours of sewing, 9 hours of painting, and 0.7 lbs. of supplies. Each Maysy doll requires 0.4 hours of sewing, 10 hours of painting, and uses 0.9 pounds of supplies. Each Dizzy doll requires 0.5 hours of sewing, 7 hours of painting, and 2 pounds of supplies. If the company earns a profit of $145 per Lexi doll, $155 per Maysy doll, and $150 per Dizzy doll, how many of each doll should the company produce to maximize profit? How much profit will result? (Use for the number of Lexi dolls, y for the number of Maysy dolls, and z for the number of Dizzy dolls.) Maximize P = subject to ≤118 ≤2805 <390.5 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes…

An online retailer requires three different size containers to package its products for shipment. The costs of these containers A, B, and C, and their capacities are shown as follows:             Container         A          B          C             Cost ($ each)     4          6          7             Capacity (cu in) 200       400      600 If the retailer orders 2500 containers with a total capacity of 1,100,000 cu in at a cost of $15,000, how many of each are in the order?

A manufacturer of table saws has three models-Deluxe, Premium, and Ultimate-that must be painted, assembled, and packaged for shipping. The table gives the number of hours required for each of these operations for each type of table saw. If the manufacturer has 104.1 hours available for painting, 360 hours for assembling, and 123.2 hours for packaging, how many of each type of saw can be produced each day? Deluxe 1.2 Painting Assembling 3 Packaging 0.4 Premium Ultimate 2 2.3 7 8 0.9 3 The manufacturer can produce deluxe saws, premium saws, and ultimate saws.

Bexter Labs produces three products: A, B, and C.Bexter can sell up to 2000 units of product A, up to 3000 units of product B, and up to 5000 units of prod-uct C. Each unit of product C uses two units of A and three units of B and incurs $7 in processing costs. Prod-ucts A and B are produced from either raw material 1 or raw material 2. It costs $9 to purchase and process one unit of raw material 1. Each processed unit of raw mate-rial 1 yields two units of A and four units of B. It costs $5 to purchase and process a unit of raw material 2.Each processed unit of raw material 2 yields one unit ofA and three units of B. The unit prices for the products are: A, $10; B, $9; and C, $32. The quality levels ofeach product are: A, 7; B, 9; and C, 6. The average quality level of the units sold must be at least 8. Deter-mine how to maximize Bexter’s profit.