A contract manufacturer has identified two customer segments for its production capacity $-$

one willing to place an order more than one week in advance and the other willing to pay a

higher price as long as it can provide less than one week's notice for production. The

customers that are unwilling to commit in advance are less price sensitive; their expected

demand under a price $p$ equals $5000-20p.$ Customers willing to commit in advance are

more price sensitive; their expected demand under a price $p$ equals $5000-40p.$ Production

cost is $c=$$$10$ per unit.

Analyze the optimal pricing strategies under the following three scenarios. Show your

calculation steps.

Assume there is no capacity constraint. If the contract manufacturer were to charge a

single price over both segments, what should the optimal price $($i$.$e$.,$ the price that

maximizes the expected profit$)$ be$?$

Assume there is no capacity constraint. What price should the contract manufacturer

charge each segment if it adopts differential pricing? How much increase in profits does

differential pricing provide?

If total production capacity is limited to $4,000$ units, what should the contract

manufacturer charge each segment under differential pricing? Solve this problem using an

optimization model. $($i$)$ Write down the optimization model formulation. $($ii$)$ Then solve it

with Excel Solver. Provide the following three screenshots of your workbook:

One screenshot of the main body of the spreadsheet with the "formula view" where

the cells show the formulas that you have implemented in them. To switch to the

"formula view" of the cells, go to the Formulas tab $>$ Formula Auditing group and click

the Show Formulas button

One screenshot of the Solver Menu settings

One screenshot of the answer report generated by Solver, with the optimal price

solutions highlighted.