Suppose a Home Improvement Contractor Is Painting the Walls and Ceiling

question 64

Multiple Choice

Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 640 cubic feet. The cost of wall paint is $0.076 per Square foot and the cost of ceiling paint is $0.19 per square foot. Let x, y, and z be the length, width, And height of a rectangular room respectively. Find the room dimensions that result in a minimum Cost for the paint. Round your answers to two decimal places.

• A) \(x = y = 8.00\) and \(z = 10.00\)
• B) \(x = y = 10.00\) and \(z = 12.80\)
• C) \(y = z = 10.00\) and \(x = 12.80\)
• D) \(x = z = 8.00\) and \(y = 10.00\)
• E) \(y = z = 8.00\) and \(x = 10.00\)

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Definitions:

Economic Profit

The financial delta observed when a business's total outgoings, including every form of cost, are removed from its total intake.

MR = MC Rule

An economic principle stating that profit maximization occurs when a firm's marginal revenue equals its marginal cost.

Short Run

In economics, a timeframe during which the quantity of at least one production factor cannot be increased.

Long Run

A period in which all factors of production and costs are variable, allowing for full adjustment to changes in market conditions.