A cinema charges $15 per ticket for a popular movie screening. The theater has a seating capacity of 300, and on average, 200 tickets are sold for each show. For every $2 decrease in ticket price, the cinema observes an additional 50 tickets sold. What should be the ideal ticket price to maximize revenue, and how many tickets would be sold at this price?

a car rental agency rents 200 cars per day at the rate of $40 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? what is the maximum income?

The Callaghan family owns 410 acres of farmland in Co. Cork on which they grow wheat and oats. Each acre of wheat costs €105 to plant, cultivate, and harvest; each acre of oats costs €210. The Bradleys have a budget of €52,500 for next year. The government limits the number of acres of oats that can be planted to 100. The profit from each acre of wheat is €300; the profit from each acre of oats is €520. The Callaghans want to know how many acres of each crop to plant in order to maximize their profit. iii. Represent the problem in graphical format and highlight the feasible region.

A group of sales reps receive bonuses if they exceed theier monthly quotas for unit sales.  Over a particular six-month period, their monthly comparisons to their quotas were:  -24, -16, +33, +12, -19, and +8 units.  How far above or below the quotas were they for the entire six-month period?

The startup cost for a restaurant is $120,000 and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?