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 variable. the cost is the variable.

Explanation:

Step1: Identify Variables

The number of posters (let's call it \( x \)) is independent because it's the quantity we can choose. Cost (\( y \)) depends on \( x \), so it's dependent.

Step2: Define Function

The cost function is \( y = 3000 + 2x \). For \( x = 1500 \), substitute: \( y = 3000 + 2(1500) \).

Step3: Calculate Cost

\( 2(1500) = 3000 \), so \( y = 3000 + 3000 = 6000 \).

Step4: Check Linearity

Each poster adds a constant $2, and setup cost is fixed. So linear model is reasonable (cost changes at a constant rate with posters).

Answer:

The number of posters is the independent variable. The cost is the dependent variable. Total cost for 1500 posters is $6000. Linear model is reasonable.