A company manufactures cellular phones and laptop computers. The company's daily production of cellular phones, c, must be more than 500,000 , and its daily production of laptop computers, l, must be more than 300,000 . If the maximum capacity of the company's manufacturing center is no more than 950,000 total cellular phones and laptop computers, which of the following systems of inequalities best models the situation described? Choose 1 answer: (A) {[c-l 950","000],[c = 500","000],[l = 300","000]:} (B) {[c-l 500","000],[l 300","000]:} (c) {[c+l = 500","000],[l = 300","000]:} (D) {[c+l 500","000],[l 300","000]:}

Question

A company manufactures cellular phones and laptop computers. The company's daily production of cellular phones, c, must be more than 500,000 , and its daily production of laptop computers, l, must be more than 300,000 . If the maximum capacity of the company's manufacturing center is no more than 950,000 total cellular phones and laptop computers, which of the following systems of inequalities best models the situation described? Choose 1 answer: (A) {[c-l > 950","000],[c >= 500","000],[l >= 300","000]:} (B) {[c-l <= 950","000],[c > 500","000],[l > 300","000]:} (c) {[c+l < 950","000],[c >= 500","000],[l >= 300","000]:} (D) {[c+l <= 950","000],[c > 500","000],[l > 300","000]:}

Bytelearn · Accepted Answer

Translate Inequalities: We need to translate the given information into a system of inequalities. The first condition is that the daily production of cellular phones, c, must be more than 500,000. This can be written as an inequality: c > 500,000.Set Production Limits: The second condition is that the daily production of laptop computers, l, must be more than 300,000. This can be written as an inequality: l > 300,000.Combine Inequalities: The third condition is that the combined total production of cellular phones and laptop computers must not exceed 950,000. This can be written as an inequality: c + l <= 950,000.Eliminate Incorrect Options: Now we need to combine these inequalities to form a system that represents all the conditions. The correct system should include all three inequalities we have written: 1. c > 500,000 (for cellular phones) 2. l > 300,000 (for laptop computers) 3. c + l <= 950,000 (for the total production capacity)Final System of Inequalities: Looking at the answer choices, we can eliminate (A) and (B) because they incorrectly use the subtraction of c and l, which does not match the third condition. We can also eliminate (C) because it uses a strict inequality (c + l < 950,000) instead of a non-strict inequality (c + l <= 950,000) for the total production capacity.The only option that correctly represents all three conditions is (D): 1. c > 500,000 2. l > 300,000 3. c + l <= 950,000 This system of inequalities matches the given conditions for the company's production.

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