Question

It typically costs a certain electronics company $130 to manufacture a certain product. However, there is one component in this product that is defective relatively often. There is a 21% chance that this component is defective, and it costs a total of $185 to manufacture the product if the component is defective.

(a) Find the expected value for the average cost for this company to produce one unit.

(b) This company's nearest competitor makes a similar product that sells for $159.99 in stores. The company's goal is to make money in the long run by selling their product, but if possible, they want to have a lower selling price than their competitor. How much should the company charge customers to purchase one unit?

Answer 1

a) probability that the component is defective is 0.21 so the probability that the component is not defective is 1-0.21= 0.79

Expected value of the cost to produce 1 unit then = 185*0.21 + 130*0.79 = $141.55

b) since the competitor sells for $159.99, inorder to sell than a lower price than the competitor and to make money, the company could charge in the range of 141.55 - 159.99

Ie greater than the expected cost but lower than the competitor so that the product sells as well as it makes profit in the long run.