Operations Management Practice Questions - Solver, Profit Maximization, Monte Carlo Simulation

Please submit your answers on this sheet as well as your Excel workbook.You need to plan which resources to use to minimize operating costs subject to the following constraints:

Maximum hydro usage is 40 MWh

Maximum carbon emission is 20 tons

Minimum dispatchable generation (coal and NG generation and solar+batteries) = 30 MWh

Minimum total MWh = 110

Maximum Solar + Batteries = 10 MWh

You cannot make partial projects – all results must be integers.

1.  What is the minimum operating cost? How much will be produced with each technology? Please paste in a screenshot of your work. 

2.  How would the results change if coal were subsidized and only cost 0.4? 

3.  What would happen if you got rid of the dispatchable generation constraint? 

You have the following information on how demand changes with price.

If the cost is 3, what price would maximize profits?  Use Excel to find an equation that fits this relationship and then use Solver to optimize profits.  Please paste in a screenshot of your work. (16)

You are starting a business installing home battery storage systems. You have the following information about the expected distribution of demand, price point per installation, equipment costs per installation, installation related fees per installation, total payroll costs, and other fixed costs. Please use Monte Carlo simulation to estimate the expected profit, minimum profit, maximum profit, and chance of profits or loss. Create a histogram of the distribution of outcomes. Please use 500 trials. Paste a screenshot of your work here. (16)

Fixed costs: $100,000

Variable costs (cost per unit produced): $15

Disposal costs per unit: $1

The market price is $40.

You are trying to figure out how much to produce to maximize profits. Please use a Monte Carlo simulation to determine which of the six production levels will maximize profits and minimize risk.  For each amount please calculate the expected profits, minimum, maximum, and % chance of loss.  Please post a screenshot of your work here. (16)

TC = 400,000 + 0.02Q + 0.0003Q²

MC = 0.02 + 0.0006Q

The market price for the good being sold is $20.

1. What level of output will maximize profits or minimize losses?

2. What are the firm’s profit or losses at this level of production and price?

3. In the short run, should this firm continue to operate or shut down? Why? 

Solver Profit Maximization

4. Assuming that all firms in this market have the same cost structure, what would be the long run equilibrium market price in theory?  

5. A monopolist faces the following monthly demand, marginal revenue, total cost, and marginal cost curves: P = 134 – 0.018Q TC = 140,000 + 0.6Q + 0.005Q²

MR = 134 – 0.036Q MC = 0.6 + 0.01Q

1. What is the profit maximizing monthly production quantity for the monopolist? (2) 

2. At what price is the good sold, given this production level? (2) 

3. What are monthly profits or losses? (2) 

4. The government wants to regulate this monopoly so that the production level increases and price decreases to where MC = Marginal Willingness to Pay (e.the demand curve). What price cap would be set, and what will be the monopolist’s output? (2)

5. What are profits or losses at this output level? (2) 

6. Instead of price regulation, the government could break up this monopoly into two competing companies, each of which will have the same cost structure as the original monopoly. Would this be a good idea? Why or why not? (Hint: Consider average cost.)(2)   

7. Using Excel, please graph the Demand Curve, the MR curve, the MC curve, and the Average Total Cost curve. Please include a legend on your graph and a title. (4)

8. Looking at the graph, at what approximate price level do you think the government should regulate this monopoly? Why?(2)   

9.  ESM Industries (ESM) has three PV system assembly plants. Currently the company purchases the subassemblies, which become part of the final product, from an outside firm. ESM has decided to manufacture the subassemblies within the company and needs to choose between renting three subassembly facilities near each of the assembly plants, or renting one central facility to serve all three assembly plants. 

A single facility with capacity of 18,000 units would have a fixed cost of $900,000 per year and a variable cost of $250 per unit. The three separate facilities would have capacities of 8,000, 6,000, and 4,000 and fixed costs of $460,000, $425,000, and $375,000 respectively, and variable costs of only $220 per unit, due to the reduction in shipping costs.

 Current production rates at the three plants are 6,000, 4,500, and 3,500 units, respectively. 

1. Assuming the current production rates do not change, which alternative should management select? (4) 

2. If demand for the final product were to increase to production capacity, which alternative would be more attractive?(2) 

3. What additional information would be useful before making a decision?(2)