Solve the Problem $x$ Will the Area of the Cross Section Be a Maximum

question 152

Multiple Choice

Solve the problem.
-A piece of rectangular sheet metal is 4 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of $x$ will the area of the cross section be a maximum (and thus maximize the amount of water that the gutter will hold) ? If necessary, round to 2 decimal places.

• A) 8 in.
• B) \(16 \mathrm { in }\).
• C) 1 in.
• D) 2 in.

---

Definitions:

AVC Curve

Stands for Average Variable Cost Curve, a graphical representation that shows the average variable costs of production at different levels of output.

ATC Curves

The graphical representation of the relationship between average total costs and output levels in the short run for a firm.

Diseconomies of Scale

Diseconomies of scale occur when a business expands to the point where the costs of managing and coordinating operations increase, leading to a rise in the average costs.

Economies of Scale

Cost advantages reaped by companies as a result of scale of operation, leading to a reduction in the per-unit cost of production.