4. Halla una serie de potencias en la forma y(x) = E=0 anx" que es una solución de la ecuación diferencial y" + 4y = 0. -4 a) an+2 (n+1)(n+2) -4 b) an+2 an (п-1)(п-2) -4 an n(n+1) -4 с) аn+2 3 an п(п-1) -4 an n(n+2) d) an+2 %3D e) ant2 %3D
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Give a clear and detailed solution of the intergral of e^-ct/m 2)1. XYZ, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each kg of fuel additive is a mixture of 2⁄5 kg of material 1 and 3⁄5 of material 3. A kg of solvent base is a mixture of 1⁄2 kg of material 1, 1⁄5 kg of material 2, and 3⁄10 kg of material 3. After deducting relevant costs, the profit contribution is P20 for every kg of fuel additive produced and P15 for every kg of solvent base produced. XYZ’s production is constrained by a limited availability of the three raw materials. For the current production period, XYZ has the following available quantities of each raw material: Raw Material Amount Available for ProductionMaterial 1 20 kgMaterial 2 5 kgMaterial 3…
- 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. Linear ProgrammingA 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.
- Y9 RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2⁄5 ton of material 1 and 3⁄5 of material 3. A ton of solvent base is a mixture of 1⁄2 ton of material 1, 1/5 ton of material 2, and 3⁄10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 33 tons Material 2 9 tons Material 3 36 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of…IF U(X,Y) IS THE SOLUTION OF THE CAUCHY PROBLEM XU\index{X}+U\index{Y}=1 U(X,0)=-X , X>0 THEN VALUE OF U(1,1) .26.Find γ so that the solution of the initial-value problem x2y″ − 2y = 0, y(1) = 1, y′(1) = γ is bounded as x → 0.