Cyclectric produces electric bikes $($e$-$bikes$)$ and for the past ten years, Cyclectric outsourced their

manufacturing process to a manufacturer in Taiwan. Despite the global supply chain that Cyclectric

has developed, they are considering if they should vertically integrate into manufacturing and produce

the e$-$bikes themselves.

In the e$-$bike industry, most manufacturing has been taking place in Asian countries, where there is

significant low$-$cost labor available to produce the products. As a result, Cyclectric is considering

setting up their own in$-$house production facility in Taiwan. However, they are not ruling out the

option to continue to outsource manufacturing $($in China$).$

Given their current supplier in China, they would not need to pay any fixed cost but would have to

guarantee to purchase $45$K units for $$875$ each.

If they decided to produce the e$-$bikes themselves in Taiwan, they would have an estimated fixed cost

of approximately $$14$ million dollars including mortgage, machinery, overhead and fixed labor

costs. The unit cost to manufacture each e$-$bike would be $$685.$

The selling price of the Cyclectric e$-$bikes would be $$1395$ each. One of their main concerns is

regarding demand. If demand is strong, the number of e$-$bikes they can sell is uniformly distributed

between $35$K and $65$K$.$ If demand is weak, the number of e$-$bikes they can sell is uniformly distributed

between $10$K and $40$K$.$ There is a $30\%$ chance that demand will be strong.

If Cyclectric chooses to continue to outsource and the demand is greater than the $45$K$,$ they can only

sell the $45$K e$-$bikes that they purchased. If demand is less than the $45$K e$-$bikes, they will only earn

revenue on the amount demanded even though they must purchase the full $45$K e$-$bikes from their

vendor.

If Cyclectric chooses to manufacture the e$-$bikes themselves, they can produce an initial $25$K e$-$bikes

and then will have the option to run a second production run of anywhere between $0$ and $40$K

additional e$-$bikes in response to market conditions. The timing of the second production run would

be shortly after Cyclectric learns if the market will be weak or strong. Thus, the total quantity that