for the following product mixprofit objective function, thesolution is:Z= 3X1 + 5X2subject to:X1 >= 5X2<= 10X1+ 2X2 >= 10a. XI= 2.8, X2= 6b. no feasible solutionc. XI= 4, X2= 3d. unboundednesse. X1=1, X2= 0

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Answered: for the following product mix profit…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A corporation manufactures candles at two locations. The cost of producing x₁ units at location 1 is C₁ = 0.02x₁² + 4x₁ +590 and the cost of producing x₂ units at location 2 is = 0.05x₂2 + 4x₂ + 200 X1 = x₂ = C₂ = The candles sell for $16 per unit. Find the quantity that should be produced at each location to maximize the profit P = 16(x₁ + x₂) - C₁ - C₂.
Please formulate the problem and show step by step
A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is C1 = 0.02x1? + 3x1 + 500 and the cost of producing x2 units at location 2 is C2 = 0.05x22 + 3x2 + 325. The candles sell for $11 per unit. Find the quantity that should be produced at each location to maximize the profit P = 11(x1 + X2) – C1 – C2. X1 X2
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32. A hardware company sells a lot of low-cost, highvolume products. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (30,000), the company can sell theproduct for $20 per unit. If sales are high (70,000),a competitor will enter and the company will be ableto sell the product for only $15 per unit. The variablecost per unit has a 20% chance of being $10, a 60%chance of being $11, and a 20% chance of being $12.Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is…

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for the following product mix profit objective function, the solution is: Z= 3X1 + 5X2 subject to: X1 >= 5 X2<= 10 X1+ 2X2 >= 10 a. XI= 2.8, X2= 6 b. no feasible solution c. X1= 4, X2= 3 d. unboundedness O e. X1=1, X2= 0