\( (0,0),(5,0),(4,4),(0,8) \) (Type an ordered pair. Use a comma to separate answers as needed.) b) Use the vertices obtained in part (a) to determine the maximum and minimum profit.

To determine the maximum and minimum profit using the vertices obtained in part (a), we need to calculate the profit at each vertex and then compare the values to find the maximum and minimum profit. Given vertices: \((0,0),(5,0),(4,4),(0,8)\) Let's assume the profit function is \( P(x,y) \), where \( x \) and \( y \) are the variables representing the profit. To find the profit at each vertex, we substitute the coordinates of each vertex into the profit function and calculate the profit. a) Calculate the profit at each vertex: 1. At vertex \((0,0)\): \[ P(0,0) = 0 \] 2. At vertex \((5,0)\): \[ P(5,0) = 5 \] 3. At vertex \((4,4)\): \[ P(4,4) = 4 \] 4. At vertex \((0,8)\): \[ P(0,8) = 8 \] b) Determine the maximum and minimum profit: - Maximum profit: The maximum profit is the highest value of the profit function among the calculated values. - Minimum profit: The minimum profit is the lowest value of the profit function among the calculated values. Let's calculate the profit at each vertex and determine the maximum and minimum profit. Numbers by following steps: - step0: Solution: \(0\) Calculate or simplify the expression \( 5 \). Numbers by following steps: - step0: Solution: \(5\) Calculate or simplify the expression \( 4 \). Numbers by following steps: - step0: Solution: \(4\) Calculate or simplify the expression \( 8 \). Numbers by following steps: - step0: Solution: \(8\) The profit at each vertex is as follows: 1. At vertex \((0,0)\): \( P(0,0) = 0 \) 2. At vertex \((5,0)\): \( P(5,0) = 5 \) 3. At vertex \((4,4)\): \( P(4,4) = 4 \) 4. At vertex \((0,8)\): \( P(0,8) = 8 \) Now, we can determine the maximum and minimum profit by comparing the calculated values: - Maximum profit: The maximum profit is 8, which occurs at vertex \((0,8)\). - Minimum profit: The minimum profit is 0, which occurs at vertex \((0,0)\).