Solve the following linear program graphically:

Maximise: $,x+4y$

$($Total Profit$)$

Subject $to$: $5x+3y,,60$

$,2x-5y,,-10$

$,x,y,,0$

$($constraint $1)$

$($constraint $2)$

$($Non$-$negativity constraint$)$

This linear program has been solved numerically using Solver in Excel and an inexperienced person has looked at the solution and believes that the following four statements to be true:

$(1)$ opportunity cost associated with $x$ is $4\mathrm{.}67($to two decimal places$)$

$(2)$ opportunity cost associated with $y$ is zero

$(3)$ shadow price associated with constraint $1$ is $1\mathrm{.}33($to two decimal places$)$

$(4)$ shadow price associated with constraint $2$ is zero

Taking each of the four statements above in turn, explain whether it is true or not and why.