Questions: Plant A can produce 8 sedans and 3 minivans per week. Plant B can produce 5 sedans and 6 minivans per week. How many weeks should each plant operate to produce at least 40 sedans? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let x be the number of weeks that plant A is producing vehicles and let y be the number of weeks that plant B is producing vehicles. Choose the correct inequality with appropriate non-negative restrictions. 8x+5y >= 40, x >= 0, y >= 0 8x+5y > 40, x >= 0, y >= 0 8x+5y < 40, x >= 0, y >= 0 8x+5y <= 40, x >= 0, y >= 0

Plant A can produce 8 sedans and 3 minivans per week. Plant B can produce 5 sedans and 6 minivans per week. How many weeks should each plant operate to produce at least 40 sedans? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let x be the number of weeks that plant A is producing vehicles and let y be the number of weeks that plant B is producing vehicles.

Choose the correct inequality with appropriate non-negative restrictions.
8x+5y >= 40, x >= 0, y >= 0
8x+5y > 40, x >= 0, y >= 0
8x+5y < 40, x >= 0, y >= 0
8x+5y <= 40, x >= 0, y >= 0

Transcript text: Plant A can produce 8 sedans and 3 minivans per week. Plant $B$ can produce 5 sedans and 6 minivans per week. How many weeks should each plant operate to produce at least 40 sedans? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let $x$ be the number of weeks that plant $A$ is producing vehicles and let $y$ be the number of weeks that plant $B$ is producing vehicles. Choose the correct inequality with appropriate non-negative restrictions. $8 x+5 y \geq 40, x \geq 0, y \geq 0$ $8 x+5 y>40, x \geq 0, y \geq 0$ $8 x+5 y<40, x \geq 0, y \geq 0$ $8 x+5 y \leq 40, x \geq 0, y \geq 0$

Solution

Solution Steps

Step 1: Define Variables

Let $x$ be the number of weeks that plant $A$ is producing vehicles and $y$ be the number of weeks that plant $B$ is producing vehicles.

Step 2: Formulate the Inequality

Plant $A$ produces 8 sedans per week and plant $B$ produces 5 sedans per week. We need to produce at least 40 sedans.

The inequality is: $8x + 5y \geq 40$

Step 3: Non-Negative Restrictions

Since the number of weeks cannot be negative, we have: $x \geq 0$ $y \geq 0$

Final Answer

The correct inequality with appropriate non-negative restrictions is: $8x + 5y \geq 40, \quad x \geq 0, \quad y \geq 0$

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 10, "ymin": 0, "ymax": 10}, "commands": ["y = (40 - 8x) / 5"], "latex_expressions": [" $8x + 5y \\geq 40$ "]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!