The following is a linear programming model for analyzing the product mix of Maxine's Hat Company, which produces three hat types: Maximize: Z$=$$ $7$ X$\_1+$$ $8$ X$\_2+$$ $6$ X$\_3$ Subject to: $2$ X$\_1+4$ X$\_2+2$ X$\_3<=120($machine A time$)5$ X$\_1+3$ X$\_2+2$ X$\_3<=400($machine B time$)2$ X$\_1+2$ X$\_2+4$ X$\_3<=110($machine C time$)$ X$\_1>=0,$ X$\_2>=0,$ and X$\_3>=0$ The POM for Windows printout below shows the optimal solution to the problem. $($a$)$ Results Screen $($b$)$ Ranging screen Consider each of the following statements independently, and state whether it is true or false. Explain each answer. A$.$ Unknown, because the optimal value of Hat $3$ should be recalculated with the new selling price. B$.$ False, because the optimal value of Hat $3$ would remain at its current value until its price increases above $ $13\mathrm{.}00.$ C$.$ True, because the reduced cost of Hat $3$ is $ $7\mathrm{.}00.$ D$.$ True, because the price of Hat $3$ increased more than $50\%$ of its current price.