The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X$1=$ number of product $1$ produced X$2=$ number of product $2$ produced

Max $250$x$1+150$x$2$

S$.$t $3$x$1+7$x$2<=175$: resource $1$

$2$x$1+5$x$2<=200$: resource $2$

x$1,$x$2>=0$

$1)$ How many units of resource $1$ are consumed by each unit of product $1$ produced? $(2$ points$)$

$2)2)$ How many units of resource two $($the second constraint$)$ are unutilized if the company produces $10$ units of product $1$ and $5$ units of product $2?(2$ points$)$

$3)$ How much profit is earned if the company produces $10$ units of product $1$ and $5$ units of product $2?(3$ points$)$

$4)$ A company uses $4$ pounds of resource $3$ to make each unit of X$1$ and $3$ pounds of resource $3$ to make each unit of X$2.$ There are only $150$ pounds of resource $3$ available. Write the constraint that reflects the relationship between X$1,$ X$2$ and resource $3.(5$ points$)$