6 A machinery supplier has a new machine which a customer is willing to buy for

Question

6 A machinery supplier has a new machine which a customer is willing to buy for $10,000, but only if it works immediately after installation. Otherwise the machine will be sent right back, and the supplier will receive nothing. The machine will only work if a key part is sufficiently flat. The supplier can send the machine as is, or first scan the surface for faults before shipment. One scan costs $500, and two scans $900. Each scan has a 90% chance ot finding a fault if it is faulty, but also has a 40% chance of falsely reporting its faulty even though it's not. Another option is to overhaul the machine before sending it at a cost of $2000. If during the overhaul the part is found not be sufficiently flat, it can be fixed for another $1000 and the supplier is then 100% sure it will work. What course of action will maximize the supplier's expected profit?

Explanation / Answer

The supplier has three options:- Send the machine as is, scan the machine(once or twice) and then decide or to overhaul the machine and then decide. Lets assume the probability of a default in a machine is p and the event is denoted by D. P(D)=p.

Scenario 1:- Sending the machine as is then the cost of sending the machine is 10,000*(1-p) where 1-p is the probability that fault is not there.

Scenario 2:- if only one scan is done, denoting the even S to be the default found by the scan, given P(S/D)=0.9,P(S/D')=0.4,then the total cost is calculated using two cases when P(S&D)*500+P(S&D')*(10500)+P(S'/D)*10500+P(S'/D')*10500=0.9*p*500+10500*(0.4*(1-p)+0.1*p+0.6*(1-p))=450p+10500*(1-0.9p)=10500-9000p

Scenario-3:- 12000*(1-p)+13000*p=12000+1000p

Thus comparing costs, we find costs in scenario 1 is least.

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.