Rewrite the objective fur Minimize w = 2y1 + 4y2 subject to: y, + y2 2 11 2у1 + Зу2 + Уз222
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A: According to guidelines we solve one question. Thanku
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- Find r and h that minimize S subject to the constraint V = 54n.Find the Optimal solution for the below Linear Program by Simplex method: Maximize Z = 200x + 80y +60z Subject to x + y + z <= 100 10x + 2y + 5z <= 600 2x + 2y + 3z <= 300 x, y, z >= 0A chemical manufacturing plant can produce zz units of chemical Z given pp units of chemical P and rr units of chemical R, where: z=160p^0.9r^0.1 Chemical P costs $400 a unit and chemical R costs $2,400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $1,440,000.A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint?Units of chemical P, p= Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production, z= units
- A firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is x2 + 600 dollars and the cost of producing y units of the same product at plant Y is given by 3y2 + 1400 dollars. If the firm has an order for 2400 units, how many should it produce at each plant to fill this order and minimize the cost of production?1) use the Lagrange multiplier to find the critical values that will optimize functions subject to the given constraints and estimate by how much the objective functions will change as a result of 1 unit change in the constant of the constraint i) Maximize Z = 2x2 - xy + 3y2 subject to x + y = 72 ii) Maximize f(x,y) = 26x – 3x2 + 5xy – 6y2 + 12y subject to 3x + y = 170 iii) Maximize f(x,y,z) = 16x2yz subject to x + y + z = 224Use the method of Lagrange multipliers to maximize the function subject to the given constraint. Maximize the function f(x, y) = x + 5y − 2xy − x2 − 2y2 subject to the constraint 2x + y = 4.
- 2. identify the feasible region and optimal solution for the linear program max z =2x1 + 3x2 s.t 1x1 + 2x2 < 6 5x1 + 3x2 < 15 x1, x2 > 0Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=2x−4yf(x,y)=2x−4y subject to the constraint x2+3y2=84x2+3y2=84, if such values exist. maximum = minimum = (For either value, enter DNE if there is no such value.)Express the problem as a system of equations using slack variables. (Use s1, s2, ... for the slack variables.) Maximize subject tofirst equationsecond equationthird equationobjective equationz =420x1 + 270x2 + 10x3, 6x1 + 7x2 + 12x3≤50 4x1 + 18x2 + 9x3≤85 x1−2x2 + 14x3≤66 x1≥0, x2≥0, x3≥0.
- A firm produces a good from two raw materials X and Y which can be bought at unit prices of pX and pY , respectively. Given a quantity x of X and a quantity y of Y , the firm can produce a quantity of goods q given by the production function q(x, y) = 3x^1/3y^2/3. The firm has a budget of $1,000 with which to buy the raw materials X and Y at unit prices of $2 and $3, respectively. Find the optimal quantities x and y that maximizes production subject to the budget constraint.Suppose an organization is manufacturing two products, P1 and P2 . The profit per tonne of the two products is $50.00 and $60.00, respectively. Both products require processing in three types of machines. The table below indicates the available machine hours per week and the time required on each machine for one tonne of P1and P2. The organization wishes to find the appropriate mix of the products in order to maximize its profit. Product 1 Product 2 Total machine hours per week Machine 1 2 1 300 Machine 2 3 4 509 Machine 3 4 7 812 Profit/tonne $50.00 $60.00 Formulate the above problem as a linear programming problem. Implement the model in part (a) in Geogebra. Determine the product mix which maximizes the profit of the company (Use both graphical and Simplex methods).