What Is the Optimal Delivery Date d to Maximize the Expected Contract Award?

[ptlnguyen]

Homework Statement

Given:
f(x) = 1/2 - 1/4 |d-x| where x is the deliver date
If the actually delivery date from target date falls within the interval of 6 < x <8, an incentive award of C results. However if x < 6, a penalty of C1 is imposed, while if x > 8, the penalty is C2. Find the value of d that maximizes the expected contract award.

Homework Equations

Please show me how to solve this problem. Thank you much.

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

Given:
f(x) = 1/2 - 1/4 |d-x| where x is the deliver date
If the actually delivery date from target date falls within the interval of 6 < x <8, an incentive award of C results. However if x < 6, a penalty of C1 is imposed, while if x > 8, the penalty is C2. Find the value of d that maximizes the expected contract award.

Homework Equations

Please show me how to solve this problem. Thank you much.

The Attempt at a Solution

What is f(x)? Is it a probability density, a cost function, a profit function or something else? If f(x) IS a probability density, it looks wrong: it must integrate to 1 when you integrate over its nonzero portions, so at the very least you need to supply bounds on x.

Anyway, the Forum rules require you to do some work on the problem yourself: we are not allowed to show you how to do it. I will say, however, that the first step---after fixing up f(x)--- must be to figure out what is the expected value of the contract award as a function of d.