Business You are screen-printing T-shirts and sweatshirts to sell at the Polk County Blues Festival and are working with the following constraints.
How many T-shirts and how many sweatshirts should you make to maximize your profit? How much is the maximum profit?
T-Shirts, x | Sweatshirts, y | Total | |
---|---|---|---|
Minutes | 10x | 30y | 1200 |
Number | x | y | 50 |
Cost | 4x | 20y | 600 |
Profit | 6x | 20y | 6x + 20y |
Objective Function: P = 6x + 20y
Organize the information in a table.
Write the constraints and the objective function.
Constraints:
How do you find the coordinates of the vertices if they are hard to read off the graph?
Solve the system of equations related to the lines that intersect to form the vertex.
Step 1
Graph the constraints to form the feasible region.
Step 2
Find the coordinates of each vertex.
Step 3
Evaluate P.
You can maximize your profit by selling 75 T-shirts and 15 sweatshirts. The maximum profit is $750.