The IUP Future Entrepreneurs Club (FEC) is selling t-shirts to raise money to fund Club activities....

 

Transcribed Image Text:

The IUP Future Entrepreneurs Club (FEC) is selling t-shirts to raise money to fund Club activities. They find that if they set their selling price at $17.20 then they will sell 39 t-shirts. They also find that for each $1.00 increase in the selling price, the Club will sell one fewer shirt. In the applet above, z represents the number of $1.00 increases in the selling price of each t-shirt, p(z) (in green) represents the selling price of the t-shirts in dollars, and R(z) (in blue) is the total revenue generated from shirt sales, in dollars. The function g(x) gives the number (quantity) of t-shirts that FEC sells. q(x) is not provided in the applet, as you will find it in one of the parts below. (a) Use the information given above to find the linear price function p(a). Alternately, you may use the applet to identify two points on the graph of p(x) and then use the points to find the linear model. P(x)=0 (b) Suppose that the FEC decides to increase the price of each t-shirt by $5.00. Then, the new selling price will be $ t-shirt sales will generate a revenue of $ This means they will sell t-shirts at the new price. and the Now, suppose instead that the FEC decides to increase the price of each t-shirt by $15.00. Then, the new selling price will be $ and the t-shirt sales will generate a revenue of $ This means they will sell t-shirts at the new price. (c) Set the z value in the input box in the applet to model the situation where the price is increased by $5.00. Using the graph of R(2), we may conclude that the revenue at this point ??? the maximum possible revenue because ??? The graph of p(z) at this point indicates The IUP Future Entrepreneurs Club (FEC) is selling t-shirts to raise money to fund Club activities. They find that if they set their selling price at $17.20 then they will sell 39 t-shirts. They also find that for each $1.00 increase in the selling price, the Club will sell one fewer shirt. In the applet above, z represents the number of $1.00 increases in the selling price of each t-shirt, p(z) (in green) represents the selling price of the t-shirts in dollars, and R(z) (in blue) is the total revenue generated from shirt sales, in dollars. The function g(x) gives the number (quantity) of t-shirts that FEC sells. q(x) is not provided in the applet, as you will find it in one of the parts below. (a) Use the information given above to find the linear price function p(a). Alternately, you may use the applet to identify two points on the graph of p(x) and then use the points to find the linear model. P(x)=0 (b) Suppose that the FEC decides to increase the price of each t-shirt by $5.00. Then, the new selling price will be $ t-shirt sales will generate a revenue of $ This means they will sell t-shirts at the new price. and the Now, suppose instead that the FEC decides to increase the price of each t-shirt by $15.00. Then, the new selling price will be $ and the t-shirt sales will generate a revenue of $ This means they will sell t-shirts at the new price. (c) Set the z value in the input box in the applet to model the situation where the price is increased by $5.00. Using the graph of R(2), we may conclude that the revenue at this point ??? the maximum possible revenue because ??? The graph of p(z) at this point indicates