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The pair of inequalities that represents the given constraints is option C. x ≤ 2y + 500 and 35x + 50y > 22,500.

The pair of inequalities that represents the given constraints is option C. x ≤ 2y + 500 and 35x + 50y > 22,500.

The first constraint states that the number of units of product A (x) should be at most 500 units more than twice the number of units of product B (y).

This is represented by the inequality x ≤ 2y + 500.

The second constraint states that the square of the company's profit is equal to the sum of 35 times the number of product A units sold and 50 times the number of product B units sold.

This is represented by the inequality 35x + 50y > 22,500.

The probable question may be:

A company manufactures two products. Market research and available resources require the following constraints:

• The number of units of product A manufactured, x, is at most 500 units more than twice the number of units of product B, y.

• The square of the company's profit is equal to the sum of 35 times the number of product A units sold and 50 times the number of product B units sold.

If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these constraints?

A.x < 2y+500

\sqrt{35x+50y}> 150

B. x< 2y+500

\sqrt{35x+50y}> 22, 500

C. x<=2y+500

35x+50y >22, 500

D. x>2y+500

\sqrt{35x+50y}> 22,500

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