A potato processing firm is supplying French fries to a fast food restaurant chain. In the short run under its current facility constraint, each day it can produce the first 1 unit for $2000 variable cost, the second unit for $1500, the third unit for $1900, the fourth unit for $2100, the fifth unit for $2500, and the six unit at $3000 to reach full capacity. The price it sells to the restaurant chain is $2500/unit. The per day (very short run) fixed cost is $1000. (Consider integer for all calculations here.)

If it has a contract to deliver 20 units in a week (no more than five days) how shall it arrange the daily production? [Hint, compare all feasible daily processing levels.] Due to competition, the restaurant chain pushes the price down to $2100/unit. Now, how shall it adjust the daily production?

What is the profit level a day now?

Realizing the market pressure, the processor decides to invest in new facility for next year (long run). Now, the processor adds a processing line at the cost of $1500 a day, while reducing its marginal cost by $500 for every unit.

What is the new optimal processing level a day?

At this level, what is the new profit?