A toy manufacturer is experiencing quality problems on its assembly line.Every defective toy that leaves the factory costs the firm $20.The firm has decided to hire quality inspectors to catch defective toys before they leave the factory. Given the above information,if the cost of each defective toy rises to $50,while inspectors are paid $150 a day,how many inspectors should the firm hire?
A)3
B)4
C)5

Question

A toy manufacturer is experiencing quality problems on its assembly line.Every defective toy that leaves the factory costs the firm $20.The firm has decided to hire quality inspectors to catch defective toys before they leave the factory.  Given the above information,if the cost of each defective toy rises to $50,while inspectors are paid $150 a day,how many inspectors should the firm hire?
A)3 
B)4 
C)5

Quizplus · Accepted Answer

Let's assume that the probability of a toy being defective is p, and the number of toys produced in a day is N. So, the cost of defective toys without inspector will be 20 * p * N. After the inspectors are hired, the cost of defective toys will be 50 * p * N + 150 * n (where n is the number of inspectors hired).
The goal is to minimize the total cost, so we need to find the value of n that minimizes the above expression. To do that, let's take the derivative of the above expression with respect to n and set it to zero:
d/dn(50 * p * N + 150 * n) = 50 * p - 150 = 0
50 * p = 150
p = 3/10
This means that 30% of the toys are defective.
Now, let's substitute the value of p in the above expression and simplify it:
Total cost = 20 * p * N (without inspector) = 20 * 3/10 * N = 6N
Total cost = 50 * p * N + 150 * n (with inspector) = 50 * 3/10 * N + 150 * n = 15N + 150n
We need to compare the above expressions and find the value of n that minimizes the second expression. We can do that by setting the two expressions equal to each other:
6N = 15N + 150n
9N = 150n
n = 6
Therefore, the firm should hire 6 inspectors to minimize the total cost.

A Toy Manufacturer Is Experiencing Quality Problems on Its Assembly