Questions: The California Almond Growers have at most 2800 boxes of almonds to be shipped from their plant in Sacramento to Des Moines and San Antonio. The Des Moines market needs at least 1000 boxes, while the San Antonio market must have at least 600 boxes. Let x= the number of boxes to be shipped to Des Moines and y= the number of boxes to be shipped to San Antonio. Complete parts (a) and (b). (a) Write a system of inequalities to express the conditions of the problem. x ≥ 1000 y ≥ 600 x+y ≤ 2800 (b) Graph the feasible region of the system.

The California Almond Growers have at most 2800 boxes of almonds to be shipped from their plant in Sacramento to Des Moines and San Antonio. The Des Moines market needs at least 1000 boxes, while the San Antonio market must have at least 600 boxes. Let x= the number of boxes to be shipped to Des Moines and y= the number of boxes to be shipped to San Antonio. Complete parts (a) and (b). (a) Write a system of inequalities to express the conditions of the problem. x ≥ 1000 y ≥ 600 x+y ≤ 2800 (b) Graph the feasible region of the system.
Transcript text: The California Almond Growers have at most 2800 boxes of almonds to be shipped from their plant in Sacramento to Des Moines and San Antonio. The Des Moines market needs at least 1000 boxes, while the San Antonio market must have at least 600 boxes. Let $x=$ the number of boxes to be shipped to Des Moines and $y=$ the number of boxes to be shipped to San Antonio. Complete parts (a) and (b). (a) Write a system of inequalities to express the conditions of the problem. \[ \begin{aligned} x & \geq 1000 \\ y & \geq 600 \\ x+y & \leq 2800 \end{aligned} \] (b) Graph the feasible region of the system.
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Solution

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Solution Steps

Step 1: Define the variables

Let x x be the number of boxes shipped to Des Moines and y y be the number of boxes shipped to San Antonio.

Step 2: Write the system of inequalities

The conditions of the problem can be expressed as: x≥1000y≥600x+y≤2800 \begin{aligned} x & \geq 1000 \\ y & \geq 600 \\ x+y & \leq 2800 \end{aligned}

Final Answer

x≥1000y≥600x+y≤2800 \begin{aligned} x & \geq 1000 \\ y & \geq 600 \\ x+y & \leq 2800 \end{aligned}

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 3000, "ymin": 0, "ymax": 3000}, "commands": ["x = 1000", "y = 600", "y = 2800 - x"], "latex_expressions": ["xgeq1000x \\geq 1000", "ygeq600y \\geq 600", "x+yleq2800x + y \\leq 2800"]}

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