Distributor of a newly launched computer monitor purchases them from a manufacturer

by placing a single order at the launch. The distributor buys the monitors for $$100$ and

sells them with a markup of $50\%$ roThe manufacturer's production cost $($not known to the

distributor$)$ of the same monitor is $$60.$ The manufacturer also has a fixed cost to

assemble and ship each batch of the monitors of $$80,000.$ Assume the demand of the

monitors is uniform between $10,000$ and $15,000,$ and the distributor can sell the unsold

monitors $($at the launch of a newer model$)$ to a discounter for $$30$ each.

$($a$)$ Assuming that the distributor orders $12,500$ monitors, what are the profits for the

manufacturer and the distributor if the actual demand turns out to be $14,000?$

$($b$)$ To encourage the distributor to place larger orders, the manufacturer enters into a

buyback arrangement with him. What is the best buyback price the manufacturer should

offer to the distributor? For that buyback price, calculate again the resulting profits for

the manufacturer and the distributor, assuming the retailer now orders $14,000$ monitors,

but the actual demand turns out to be $12,000.$ You can assume that the manufacturer

can also salvage the unsold monitors he buys back from the distributor at the same

price.

$($C$)$Assuming the profit margin for the distributor is his stock$-$out cost, and given the

marginal loss for each unsold monitor, what service level should the distributor target

under the buyback contract?