Develop a simulation for the following problem. The management of Madeira Manufa
ID: 3931977 • Letter: D
Question
Develop a simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is uniformly distributed between $16 and $24 per unit. The product will sell for $50 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1200 units and a standard deviation of 300 units. Use simulation trials to answer the following questions: What is the mean profit for the simulation? What is the probability that the project will result in a loss? What is your recommendation concerning the introduction of the product?Explanation / Answer
a) and b)
import numpy as np #importing numpy to use normal and uniform distribution functions
mu = 1200
sigma = 300
number_of_simulations = 1000
simulations = np.random.normal(mu, sigma, number_of_simulations) #creating 1000 simulations for #number of units sold
negative_profits = 0 #initialising the number of losses
profit_from_all_simulations = 0
initial_cost = 30000 #fixed setup cost
for simulation in simulations: #single simulation
simulation = int(simulation)
product_costs = np.random.uniform(16,24,simulation) #uniform distribution of cost of a unit
total_production_cost = sum(product_costs) #summing the total production cost
profit = 50*simulation - total_production_cost - initial_cost #calculating profit
profit_from_all_simulations += profit
if profit<0:
negative_profits += 1
print "Mean Profit:", profit*1.0/number_of_simulations
print "Probability of loss:", negative_profits*1.0/number_of_simulations
c) The product should not be introduced since the mean profit is almost negligible and the probability of loss is high (>25%).
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