Suppose that at the beginning of the year a Vermont maple sy

Suppose that at the beginning of the year, a Vermont maple syrup distributor found that the demand for maple syrup, sold at $15 a quart, was 300 quarts each month. At that time, the price was going up at a rate of $0.50 per month, but despite this, the demand was going up at a rate of 20 quarts per month due to increased advertising (a) Find an equation that models price per quart of syrup t months after the start of the year. (b) Find an equation that models demand (in quarts) t month after the start of the year. (e) Find an equation that models total revenue t months after the start of the year. (d) How fast was the reverse increasing three months into the year?

Solution

Demand after T months will be

300+20*t

Now price of The syrup = 15+0.5t

So Revenue will be P*D = (15+0.5t)*(300+20*t) in that particular month