Develop a simulation for the following problem The managemen

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?

Solution

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%).