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[35 points] Haier and Geli are two Chinese manufacturers of home appliances that have merged. They have their own markets in Europe. Haier has plants in France, Germany, and Finland, whereas Geli has plants in the United Kingdom and Italy. The European market is divided into four regions: North, East, West, and South. Plant capacities (millions of units per year), annual fixed costs (millions of euros per year), regional demand (millions of units), and variable production and shipping costs (euros per unit) are shown in the table below.       North   East   South   West   Capacity (M of Units) Annual fixed cost (M$) Haier France 100 110 105 100 50 1000   Germany 95 105 110 105 50 1000   Finland 90 100 115 110 40 850 Demand   30 20 20 35     Geli U.K. 105 120 110 90 50 1000   Italy 110 105 90 115 60 1150 Demand (M of units)   15 20 30 20     a. Prior to the merge, if Haier sets an objective of minimizing the total costs while satisfying all market demands (no shortage), how should its network be structured (providing all plants remain open)? i. [5 points] Define all the decision variables and cost parameters you need to construct the model. ii. [10 points] Set up the optimization model and write the mathematical formulation, including the objective function and all constraints. iii. [5 points] Solve the model in Excel and briefly describe the optimal solution you found.   b. [15 points] After the merge, how should the new network be structured to satisfy all market demands (no shortage), if the merged company sets the objective of minimizing the total fixed and variable costs? In this scenario, considering that plants may open or close and markets may receive products from one or more plants. Solve the model in Excel and briefly describe the optimal solution you found.

I understand that failure to submit my written work to payned@atc.edu, within 5 minutes of submitting this test, will result in a 0 score for any questions that required calculations. To receive full credit, I further understand that I must include any formulas used, replacement of variables with appropriate numerical data, and circled correct final result with appropriate units and number of significant figures. My work must be legible, numbered, and named.Write your initials in space below to acknowledge your understanding.

At a given temperature, K = 0.024 for the equilibrium:PCl5(g)    PCl3(g) + Cl2(g)What is K for:Cl2(g) + PCl3(g)    PCl5(g)?This problem requires calculations on submitted scratch paper.Hint: Determine mathematical relationship of both chemical equations to determine new value of K

The reaction A → B follows first-order kinetics with a half-life of 21.7 hours. If the concentration of A is 0.023 M after 48.0 hours, what was the initial concentration of A?This problem requires calculations submitted on scratch paper.

Given the following equilibria, Ni2+(aq) + 2 OH–(aq) Ni(OH)2(s) K1 = 1.8 × 1015 Ni2+(aq) + 4 CN–(aq) Ni(CN)42–(aq) K2 = 2.0 × 1031   determine the equilibrium constant, Kc, for the following reaction.  Kc = ?Ni(OH)2(s) + 4 CN–(aq) Ni(CN)42–(aq) + 2 OH–(aq)This problem requires calculations submitted on scratch paper.

A flexible vessel contains 14.00 L of gas at a pressure of 1.27 atm. Under the conditions of constant temperature and constant number of moles of gas, what is the volume of the gas when the pressure of the vessel is decreased by a factor of two?Show Required Work

What is the Kc expression for the equilibrium given below?CuI(s) Cu+(aq) + I−(aq)

Write Kp expression for the following reaction:2 H2O2 (g) ⇔ 2 H2O (g) + O2 (g)You may write the answer in your scratch paper if you prefer that over typing.

There are 5 engineering male students and 2 engineering female students standing together in a line to have photos taken. If the two female students can not be at ends (neither of the two will be at the ends), how many different ways of orders do they have ? 

There are 5 engineering male students and 2 engineering female students standing together in a line to have photos taken. If the two female students must be at both ends of the line, how many different ways of orders can they follow when taking photos ?