Question 2. TJ runs a side business called TJ's Tikoy Shop that becomes busy every year around the New Year selling tikoy (rice cakes/). To prepare for the rush, he hires extra staff to help fill the order. Each additional staff member is paid at the rate of $20 per hour, and can produce 40 orders per hour. Moreover, staff need to be provided with adequate safety equipment at work, which costs TJ $30 per staff member, and a supervisor needs to be hired at a rate of $27 per hour to help manage staff. Based on historical data, TJ has modeled the demand for tikoy using the equation q= 1200+80(30-p) where p is the price of each order and q is the quantity demanded in number of orders. The cost of raw ingredients, packaging, and shipping depends on quantity produced, and come out to a total of $10 per order. Meanwhile TJ also incurs a fixed cost of $500 for the entire operation (for social media advertising, etc). (a) If TJ sets the price at $30 per order, determine the number of staff TJ should hire in order to incur the minimum possible cost. (b) TJ is having a hard time finding staff to work during the holidays, and can only hire three regular staff (and one supervisor). Now find the price point p that will maximize the shop's profit.

Fig: 1