Determine the total production amount

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Reference no: EM132249475

Operation Research Question -

Use Lagrange multiplier to solve the question.

Consider a global manufacturer who sells its products in two markets. The first market, Country 1, is the home country. The other one, Country 2, is an international location with a different currency with exchange rate e. The exchange rate is the value of the home country currency (Currency 1) that is equivalent to one unit of the foreign country (Country 2) currency. Suppose that demand at each market is a decreasing function of price (in local currency) and given as follows:

D₁ = α₁ - p₁ and D₂ = α₂ - p₂

where α₁ and α₂ are parameters representing the demand potential in each market. Prices must be set in local currencies in each market. The manufacturer produces all the goods in the home country. The unit production cost is c. The manufacturing facility has a capacity of K. The manufacturer pays t for each unit transported to the foreign market in home country currency.

A) Develop an optimization model that maximizes the manufacturer's total profit. Determine the total production amount, allocation of products to markets, and pricing at each market.

B) Consider the following scenarios and remodel the problem for each scenario. Suggest solution approaches.

Scenario I: Suppose that the manufacturing lead time is relatively long and thus, during production the exchange rate can either up or low. The manufacturer must commit to the total production amount before it observes the future exchange rate. However it allocates the products to markets and determines prices after selling season exchange rate is realized. It is forecasted that the exchange rate will go down to e_L with probability q, and will go up to e_H with probability (1 - q).

Scenario II: Suppose now that the products must be produced and shipped (allocated) to markets before the exchange rate is realized. However, pricing still can be delayed after the realization of the exchange rate. As in the previous case, it is forecasted that the exchange rate will go down to e_L with probability q, and will go up to e_H with probability (1 - q).

C) Conduct a numerical analysis and compare optimal policies in the base case, Scenario I, and Scenario II. How do exchange rate uncertainty and timing of commitment affect the manufacturer's profits?

Attachment:- Assignment Files.rar

Reference no: EM132249475

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