using demand and cost functions to determine the optimal quantity, price, and profit for a company distributing organic cocoa powder, and then analyzing how changes in external factors, such as the COVID-19 pandemic, can affect these values.

A company distributes organic cocoa powder with a monthly demand function ofQ =80,000–2,000p, and total costfunctionTC =12,000+15Q + 0.002Q2, where p ist he price of organic cocoa powder per pound(dollars)and Q is the quantity (pounds).
(a) What are the optimal quantity, price, and profit of the company?
(b) Since the COVID-19 pandemic, most employees started working from home, so the
company cut down its rent of office building by $2,000 per month. What are the optimal
quantity, price, and profit under the new condition?