Business and Economics Case Study

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1. As CEOs of a company trying to find the most suitable supplier to purchase raw materials, we will focus our decision on the amount of impurity that the material contains. In order to do that, we will base our criteria in the analysis of a consignment of raw materials from both supplier A and supplier B in terms of its impurity level – this must not exceed 5%.

In order to compute these probabilities we need to standardize to get values from the available tables (Exhibit 1). After performing these computations, we got two probability levels of reaching an impurity level below 5%, from the different suppliers: for supplier A it was 93% (on average, 93 times out of 100, it will have an impurity level below 5%) and of 91% for supplier B (on average, 91 times out of 100, it will have an impurity level below 5%). So, supplier A is the one that most probably will meet our needs.

1. After choosing supplier A, the company decided to create a clause stating that six times per year, a sample of 16 consignments will be tested, in order to control the level of impurities. Out of this six tests, if at least 2 of them exceeded 4.5% of average value of impurities, the supplier would have to pay a compensation of 1000€. However, if it is not the case, the supplier would be compensated with 300€ for each sample destroyed.

Firstly, we computed the sampling distribution of the average of 16 consignments (), and then the probability of it being greater than 4.5% (Exhibit 2). After performing these computations, we got a probability level of 15.87% - this means that, on average, 15.87 times out of 100 the value of impurities is greater than 4.5%. Initially the random variable followed a normal distribution; However, now we may analyze this problem as a discrete variable, in which we assess if a box has an average value of impurities greater than 4.5% or not. As such, we created a new binomial variable (Y) that represents the number of rejected boxes in the 6 tests (N=6), with a probability of success of 15.87% - the probability of a box having a percentage of impurities larger than 4.5%. This binomial variable follows a binomial distribution (Exhibit 3).[pic 4]

After computing the probability of two boxes being rejected (Exhibit 4), one may expect that, on average, 24.41 out of 100 times, the clause would be broken and the supplier would have to compensate the company in 1000€. Therefore, the expected return of this clause would be 1116.52€ - on average, 24.41 out of 100 times, supplier A would have to pay 1000€, and on 75.59 out of 100 times, the supplier would receive 300€ per sample destroyed (Exhibit 5). Since the expected return is positive, supplier A’s CEO should accept this clause.