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: 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 companys profit is equal to the sum of 35 times the number of units of product a and 50 times the number of units of product b sold. if the company expects weekly profits to exceed $22,500, which pair of inequalities represents these constraints? \n$xgeq2y + 500$ $sqrt{35x+50y}>22,500$ \n$x<2y + 500$ $sqrt{35x+50y}>22,500$ \n$x<2y + 500$ $35x + 50y>22,500$ \n$x<2y + 500$ $sqrt{35x+50y}>150$

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 companys profit is equal to the sum of 35 times the number of units of product a and 50 times the number of units of product b sold. if the company expects weekly profits to exceed $22,500, which pair of inequalities represents these constraints? \n$xgeq2y + 500$ $sqrt{35x+50y}>22,500$ \n$x<2y + 500$ $sqrt{35x+50y}>22,500$ \n$x<2y + 500$ $35x + 50y>22,500$ \n$x<2y + 500$ $sqrt{35x+50y}>150$

Answer

Explanation:

Step1: Analyze the profit - related constraint

The company's profit is the sum of 35 times the number of product A units ($35x$) and 50 times the number of product B units ($50y$), and the profit is expected to exceed $22,500$. So the profit - related inequality is $35x + 50y>22500$.

Step2: Analyze the production - related constraint

The number of units of product A, $x$, is at most 500 units more than twice the number of units of product B. So the production - related inequality is $x\leq2y + 500$.

Answer:

The pair of inequalities that represents the constraints is $x\leq2y + 500$ and $35x+50y > 22500$.