Explanation Given information: A company produces and sells shirts. The fixed costs are $7000 and the variable costs are $5 per shirt. Shirts are sold for $12 each Concept Used: Cost function: The cost function, C ( q ) gives the total cost of producing a quantity q of some good. The more goods that are made, the higher the total cost, so C is an increasing function. Cost of production can be separated into two parts: the fixed costs, which are incurred even if nothing is produced and the variable costs, which depend on how many units are produced. T o t a l c o s t s f o r t h e c o m p a n y = F i x e d c o s t s + V a r i a b l e C o s t The variable cost for one additional unit is called the marginal cost. For a linear cost function, the marginal cost is the rate of change, or slope, of the cost function. The Revenue Function: The revenue function, R (q) gives the total revenue received by a firm from selling a quantity, q, of some good. If the good sells for a price of p per unit, and the quantity sold is q, then R e v e n u e = P r i c e ⋅ Q u a n t i t y The profit function: P r o f i t = R e v e n u e − C o s t The break-even point for a company is the point where the profit is zero and revenue equals cost. Calculation: Steps Description V a r i a b l e C o s t = C o s t P r i c e / s h i r t ︷ 5 × N u m b e r To determine (b) To find: The quantity of shirts and profit at the given price To determine (c) To find: Cost, revenue and profit as functions of price, p using the demand function To determine (d) To graph: Profit against price and find the price that maximizes profit and profit.

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 1.4, Problem 29P

To determine

(a)

To find:

The cost and revenue as functions of the quantity of shirts, q.

To determine

(b)

To find:

The quantity of shirts and profit at the given price

To determine

(c)

To find:

Cost, revenue and profit as functions of price, p using the demand function

To determine

(d)

To graph:

Profit against price and find the price that maximizes profit and profit.

Expert Solution & Answer

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Chapter 1.4, Problem 28P

Chapter 1.4, Problem 30P

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Chapter 1 Solutions

APPLIED CALCULUS (WILEY PLUS)

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(a) To find: The cost and revenue as functions of the quantity of shirts, q.

Solution Summary: The author explains the cost and revenue functions of the quantity of shirts, q. The fixed and variable costs are 7000 and 5 per shirt.

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(a) To find: The cost and revenue as functions of the quantity of shirts, q.

(b) To find: The quantity of shirts and profit at the given price

(c) To find: Cost, revenue and profit as functions of price, p using the demand function

(d) To graph: Profit against price and find the price that maximizes profit and profit.

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Chapter 1 Solutions

(a)

To find:

The cost and revenue as functions of the quantity of shirts, q.

(b)

To find:

The quantity of shirts and profit at the given price

(c)

To find:

Cost, revenue and profit as functions of price, p using the demand function

(d)

To graph:

Profit against price and find the price that maximizes profit and profit.