Reference no: EM132657509

Problem 1:  

SleazeCo manufacturers wind turbines (that produce electricity) for sale in Texas. They currently have one manufacturing facility in Dallas, Texas, that has the following total cost curve:

TC_D = 10,000,000 + 150,000*q_D + 25(q_D)² , where q_D is the number of turbines produced per year in Dallas and TC_D is the total cost in dollars.

While these turbines are fairly standard in design, the SleazeCo brand is well-regarded and has some market power. In fact, the demand and marginal revenue curves for SleazeCo is given by

Demand:                             P = $350,000-5q,

Marginal Revenue:         MR = $350,000 - 10q,

where q is the total amount SleazeCo sells, P is the price (in dollars) and MR is the marginal revenue (in dollars).

Questions:

1. What is the profit maximizing price SleazeCo's should set for its turbines?  

2. What is its profit at this price?

3. Gus Ty, the manager of SleazeCo's turbine business, has done some analysis and has found a facility in Houston, Texas, that, after some alterations, could also be used for manufacturing. Its total cost is given by

TC_H = 12,000,000 + 140,000q_H + 20(q_H)², where q_H is the number of units produced at this plant and TC_H is the total cost in dollars.

Should Gus build the second facility? Why? Justify your answer with relevant numbers and analysis. Note: a suitable and complete answer will show whether the profits of the SleazeCo turbine business increase or decrease with the new plant if Gus operates both plants optimally. Hint: If Gus is going to produce optimally at both plants, what must be true about the marginal cost at one versus the other? If they are different, is that a problem?

Problem 2:

Recall that SleazeCo also manufacturers residential air conditioning units in Ohio and sells them in Michigan and in Arizona. These units are fairly unique in that they are very energy efficient and are in demand by households that are concerned about global warming and want to be "green." The demand curve for these units in Michigan is described by , where  is the price per unit in thousands of dollars and is the number of units (in thousands). The demand curve in Arizona is described by , where is the price per unit (in thousands) and  is the number of units (in thousands). The company produces these in one plant in Ohio that has the following total cost function:

where  is the quantity in thousands and  is in thousands. Although Arizona is farther away from Ohio than Michigan is from Ohio, assume the transportation costs (for delivery) is the same and, for simplicity, equal to zero.  

Questions:

1. How many units should the company make? _______________

2. What price should it charge in Arizona?           _______________

3. What price should it charge in Michigan?      _______________

4. What is the profit on these products? _____________________