Suppose a company produces two public goods: A and B. The equation of the PPF is 5x^2+6y^2=8,870 where x and y are the quantity of public goods A and B, respectively.This year, the company produces 32 units of Good A and 25 units of Good B. How much of Good B will the company produce if, as a result of economic growth the number of available resources increases by 5,850 and the quantity of Good A is the same? Enter your answer in the box below and round to the nearest whole number if necessary. Answer 2 Points square unit(s)

To solve this problem, we need to determine the new production possibility frontier (PPF) equation after the increase in available resources and then find out how much of Good B can be produced while keeping the quantity of Good A constant at 32 units.<br /><br />1. **Original PPF Equation:**<br /> \[<br /> 5x^2 + 6y^2 = 8,870<br /> \]<br /><br />2. **Increase in Resources:**<br /> The resources increase by 5,850, so the new PPF equation becomes:<br /> \[<br /> 5x^2 + 6y^2 = 8,870 + 5,850 = 14,720<br /> \]<br /><br />3. **Substitute \( x = 32 \) into the New PPF Equation:**<br /> \[<br /> 5(32)^2 + 6y^2 = 14,720<br /> \]<br /> \[<br /> 5 \times 1024 + 6y^2 = 14,720<br /> \]<br /> \[<br /> 5120 + 6y^2 = 14,720<br /> \]<br /> \[<br /> 6y^2 = 14,720 - 5120<br /> \]<br /> \[<br /> 6y^2 = 9,600<br /> \]<br /><br />4. **Solve for \( y^2 \):**<br /> \[<br /> y^2 = \frac{9,600}{6}<br /> \]<br /> \[<br /> y^2 = 1,600<br /> \]<br /><br />5. **Calculate \( y \):**<br /> \[<br /> y = \sqrt{1,600} = 40<br /> \]<br /><br />Therefore, if the company keeps producing 32 units of Good A, it can produce 40 units of Good B with the increased resources. <br /><br />The answer is \(\boxed{40}\) units.