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- Suppose a maquiladora with two types of parts as raw material: type A and type B. In a first stage of assembly using A and Bs the weapon types are produced two M and N. In a second stage of assembly using the types M and N the types of reinforcements X and Y are produced. knows that to assemble 4 Xs and 3 Ys, a total of 38 Ms and 20 Ns and that to assemble 4 Xs and 1 Ys were required in total 26 Ms and 12 Ns. Furthermore, it is known that to obtain an M requires 4 As and 4 Bs and for an N requires 1 As and 2 Bs. Indicate, in order, how many A and B pieces required to build an X and how many to build a Y. Determine: A) the system of linear equations that models the previous context. B) the solution of the system using some SEL solution method seen in class (example: Gaussian elimination; Gauss-Jordan; Cramer's rule, etc.). C) Respond to the problem raised.Assume that the production of 1 unit of magnesium requires 0.8 units of magnesium and 0.2 units of aluminum, and that the production of 1 unit of aluminum requires 0.3 units of magnesium and 0.2 units of aluminum.An oil refinery produces low-sulfur and high-sulfur fuel. Each ton of low-sulfur fuel requires 5 minutes in the blending plant and 4 minutes in the refining plant; each ton of high-sulfur fuel requires 4 minutes in the blending plant and 2 minutes in the refining plant. If the blendiing plant is available for 3 hours and the refining plant is available for 2 hours, how many tons of each type of fuel should be manufactured so that the plants are fully used?
- Can u plz provide its solution?A chemical manufacturer wants to lease a fleet of 22 railroad tank cars with a combined carrying capacity of 414,000 gallons. Tank cars with three different carrying capacities are available: 9,000 gallons, 18,000 gallons, and 36,000 gallons. Letting t = number of 36,000 railroad tank cars in the fleet, 2t -2 9,000 gallon railroad tank cars, and -3t+24 18,000-gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing 9,000-gallon tank car is $250 per month, 18,000-gallon tank car is $750 per month, and a 36,000-gallon tank car is $1350 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leading costSuppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows into the second lake, and then water from the second lake flows further downstream. The in and out flow from each lake is 500 liters per hour. The first lake contains 100 thousand liters of water and the second lake contains 200 thousand liters of water. A truck with 500 kg of toxic substance crashes into the first lake. Assume that the water is being continually mixed perfectly by the stream. a) Find the concentration of toxic substance as a function of time in both lakes. b) When will the concentration in the first lake be below 0.001 kg per liter? c) When will the concentration in the second lake be maximal?
- A company manufactures two products such as X and Y using machines A and B. Each X While the product is processed in machine A for 50 minutes, it is processed in machine B for 30 minutes. Each Y product is processed for 24 minutes on machine A, while 33 minutes on machine B sees .. At the beginning of the week, there are 30 X products and 90 Y products in the warehouse. Machine A can work 40 hours a week, while machine B can work 35 hours a week. At the weekend, 75 orders of X products and 95 orders of Y products will be sent to the customer. The aim of the company is to ensure that the X and Y products in the warehouse are to MAXIMIZE the total number. Find the objective function. Also find the production numbers of x and y.In a rural area, there is a road that connects location X and location Y, however this road cannot be passed about 50% of the time due to floods. There is another route that goes to location Z. The road from location X to Z is only passable 75% of the time and the road from location Z to Y is only passable 70% of the time. Furthermore, if the road between location X and Z is passable, then the road travelling from Z to Y is passable 80% of the time. If the route from location X to Y to Z is passable, then the route directly from location X to Y is passable 80% of the time. What is the probability of travelling from location X to Y? If during the night a flood makes the road from X to Z impassable, what is the probability that the traveller can still travel from Z to Y? Please answer completely will give rating surelyA company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. Solve the above problem by using Simplex Method. Linear Programming
- A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. Solve the above problem by using Simplex Method.A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a Linear programming model.A diesel engine uses type A filter and high-grade lubricating oil costing P55 per liter. With this filter, the oil and the filter have to be changed every 500hrs. of operation, and 5L of oil have to be added every 100hrs. This filter costs P1480 a piece. Eighty liters of oil fill the engine. Another type, filter B, costing of P1200 may be used with a lower grade of oil costing P48 per liter. However, if this filter is used, the oil and filter have to be changed every 300hrs and 10 liters are added after each 150hrs the engine is used. Hint: Consider the cost per hour.
