GMAT Inequalities: What is the maximum number of balls…

7 x + 6 y \leq 38, 000 4 x + 5 y \leq 28, 000 A manufacturer wants to produce x balls and y boxes. Resource constraints require that x and y satisfy the inequalities shown. What is the maximum number of balls and boxes combined that can be produced given the resource constraints?

inequalities

Explanation	Calculations	Help
$We first name the variables to match the question.$	$x = number of balls y = number of boxes$
$We sum the two resource constraints "7x + 6y \leq 38000" and "4x + 5y \leq 28000", applying Adding Two Inequalities .$	$7 x + 6 y \leq 38000 4 x + 5 y \leq 28000 11 x + 11 y \leq 66000$
$We divide both sides of the combined inequality by 11, which is positive, so the inequality direction stays the same according to Multiplying/Dividing Inequalities by Positive .$	$\frac{11 x + 11 y}{11} \leq \frac{66000}{11} x + y \leq 6000$
$We verify that the bound is attainable by finding values that satisfy both original constraints.$	$7 \times 2000 + 6 \times 4000 = 38000 4 \times 2000 + 5 \times 4000 = 28000 x + y = 2000 + 4000 = 6000$

6,000 (B)

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