problem 1) Chemical manufacturer sells ammonia at a price of 560 dollars per unit. The daily total production cost in dollars for x units is given by 10000+20*x+1/50*x^{2} and daily production capacity is at most 14,000 units.
How many units of ammonia (rounded to nearest whole number using the round command) should be manufactured and sold daily to maximize profit? Use Optimization[Maximize].
How much money (rounded to the nearest dollar) would be made each day for that amount of production?
As time goes on and economy changes, manufacturer knows that price of ammonia could change quickly. In order to prepare for future price changes, manufacturer collected the list of prices that ammonia can be sold for in the future. The price list is as follows:
[570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 680, 690, 700, 710, 720, 730, 740, 750, 760, 770, 780, 790, 800, 810, 820, 830, 840, 850, 860]
For each unit price, and cost function described in part (a), determine the amount that must be produced to maximize profit, rounded to nearest whole number. Use Optimization[Maximize]. The result must be the list of integers (numbers without decimal points). Do not forget to take into account the daily production limit of 14,000 units. This list might contain duplicate values.