Problem $1$

In an effort to exercise better controls over shipping costs, Mesa Technologies has prepared the following summary:

$\backslash$table$[[,,$Information about Shipped Units$],[$Month$,\backslash$table$[[$Shipping$],[$Costs$]],$Number of units shipped,$\frac{\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}}{(inlbs.)},$Sales value of shipped units$],[$May$,$$$5,000,4,500,3,000,$$$80,000],[$June$,$$$7,700,5,300,5,000,$$$95,000],[$July$,$$$6,200,5,700,4,000,$$$105,000],[$August$,$$$10,400,9,500,7,000,$$$170,000],[$September$,$$$8,600,7,000,6,000,$$$132,000],[$October$,$$$4,200,7,300,4,500,$$$135,000]]$

Mesa's monthly production and shipping capacity is $10,000$ units $($or $8,000$ pounds$).$ After detailed analysis, their logistics analysts have determined that the best predictor of shipping costs is the weight $($in lbs$.)$ of units shipped.

Required

A$.$ Give a short definition for each of the following: $($a$)$ Total fixed costs, $($b$)$ Total variable costs, and $($c$)$ Total mixed costs. In your definitions, explain how the total cost changes with changes in productive activity, i$.$e$.,$ as the company produces more $($or fewer$)$ units, how does the amount of cost for the total cost item change with increases $($decreases$)$ in the production.

B$.$ Using the high$-$low method and weight $($in lbs$.)$ of units shipped as the $x-$variable, develop a cost estimation equation for monthly shipping costs. $($Please show your work$)$

C$.$ Using your equation from B$.$ above, predict shipping cost for a month in which the company ships: $($a$)4,000$ lbs$.,($b$)7,000$ lbs$.$ and $($c$)9,500$ lbs$.$

D$.$ If Mesa's analyst used average cost per pound to determine the cost to ship $7,800$ pounds of goods, the estimated cost would differ from your estimate, i$.$e$.,$ based on your cost estimation equation. Give a brief explanation of why your estimation equation derives a result different from a cost estimation result derived from average cost?$w$