a company manufactures two products. market research and available resources require the following…

a company manufactures two products. market research and available resources require the following constraints:\n- 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).\n- the square of the companys 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.\nif the company expects weekly profits to exceed $22,500, which pair of inequalities represents these constraints?\n\n(xleq2y + 500)\n(35x+50y>22,500)\n\n(xgeq2y + 500)\n(sqrt{35x + 50y}>22,500)\n\n(xleq2y + 500)\n(sqrt{35x + 50y}>22,500)\n\n(xleq2y + 500)\n(sqrt{35x + 50y}>150)

a company manufactures two products. market research and available resources require the following constraints:\n- 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).\n- the square of the companys 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.\nif the company expects weekly profits to exceed $22,500, which pair of inequalities represents these constraints?\n\n(xleq2y + 500)\n(35x+50y>22,500)\n\n(xgeq2y + 500)\n(sqrt{35x + 50y}>22,500)\n\n(xleq2y + 500)\n(sqrt{35x + 50y}>22,500)\n\n(xleq2y + 500)\n(sqrt{35x + 50y}>150)

Answer

Explanation:

Step1: Translate the first constraint

The number of units of product A ($x$) is at most 500 units more than twice the number of units of product B ($y$). So, $x\leq 2y + 500$.

Step2: Translate the second - profit constraint

Let $P$ be the profit. Given that $P^{2}=35x + 50y$, and the company expects weekly profits to exceed $$22500$. So, $P>22500$. Since $P = \sqrt{35x + 50y}$, we have $\sqrt{35x+50y}>22500$.

Answer:

$x\leq 2y + 500$, $\sqrt{35x + 50y}>22500$