A retail store sells a product that has a variable cost of $$(3+$n$)$ a unit with n in the interval $[1$;

$10].$ Fixed costs are $$(10,000+$p$)$ per month with p in the interval $[1,000$; $20,000].$ The store manager estimates that if the price is set at $$5$ a unit, the sales volume will be $1,200-5$x units per month with $*$ denoting the selling price.

$1.$ What will be the sales volume if the retailer sets the selling price $\backslash$times at $$(10+$n$),$ n being a value that you choose according to the instruction above $($defined earlier? Which price should be set for the retailer to sell $600$ units?

$2.$ After presenting the related equations, draw, on the same diagram, the lines or curves of

$($i$)$ demand curve, $($il$)$ total revenue, $($ili$)$ total cost and $($iv$)$ profits $($all as functions of the output$).$ Do not forget to provide the scales used.

$3.$ Find the break$-$even quantity when the selling prices are $$10$ and $$6$ respectively. Which price is the most attractive to the manager? Justify your answer.