Question

the cost of publishing a poster is $3000 for setting up the printing equipment, plus $2 per poster printed. this situation can be modeled by a linear function. identify the independent and dependent variables. draw a graph of the function, then use the graph to find the total cost to produce 1500 posters. is a linear model reasonable for this situation? the number of posters is the independent variable. the cost is the dependent variable. use the graphing tool to graph the line. the cost to produce 1500 posters is $\square$.

Explanation:

Step1: Identify the cost function

The fixed cost is $3000, and the variable cost is $2 per poster. So the cost function \( C(n) = 3000 + 2n \), where \( n \) is the number of posters.

Step2: Substitute \( n = 1500 \)

Substitute \( n = 1500 \) into the function: \( C(1500)=3000 + 2\times1500 \)

Step3: Calculate the cost

First, calculate \( 2\times1500 = 3000 \), then \( 3000+3000 = 6000 \). Alternatively, from the graph, when \( n = 1500 \), we can find the corresponding cost on the y - axis. Looking at the graph, the line has a y - intercept of 3000 (when \( n = 0 \), cost is 3000) and a slope of 2. For \( n = 1500 \), moving 1500 units along the x - axis (number of posters) from \( n = 0 \), with a slope of 2, the increase in cost is \( 2\times1500=3000 \). Adding the fixed cost 3000, we get \( 3000 + 3000=6000 \).

Answer:

6000