$2-17$ Variable costs and fixed costs. Combined Minerals $($CM$)$ owns the rights to extract minerals from beach sands on Fraser Island. CM has costs in three areas:

a$.$ Payment to a mining subcontractor who charges $$90$ per ton of beach sand mined and returned to the beach $($after being processed on the mainland to extract three minerals: ilmenite, rutile, and zircon$).$

b$.$ Payment of a government mining and environmental tax of $$30$ per ton of beach sand mined.

e$.$ Payment to a barge operator. This operator charges $$140,000$ per month to transport up to $100$ tons of beach sand per day to the mainland and then return to Fraser Island $($i$.$e$.,0-100$ tons per day $$140,000$ per month; $101-200$ tons per day $=$ $$280,000$ per month; etc.$).$

Each barge operates $25$ days per month. The $$140,000$ monthly charge must be paid even if fewer than $100$ tons are transported on any day and even if CM requires fewer than $25$ days of barge transportation in that month.

Required

CM is currently mining $180$ tons of beach sand per day for $25$ days per month.

$1.$ What is the variable cost per ton of beach sand mined? What is the fixed cost to CM per month?

$2.$ Plot a graph of the variable costs and another graph of the fixed costs of CM$.$ Your graphs should be similar to Exhibit $2-3,$ Panel A $($page $32),$ and Exhibit $2-4($page $35).$ Is the concept of relevant range applicable to your graphs? Explain.

$3.$ What is the unit cost per ton of beach sand mined $($a$)$ if $180$ tons are mined each day and $($b$)$ if $210$ tons are mined each day? Explain the difference in the unit$-$cost figures.