This document contains a math test with 4 questions. Question 1 asks students to solve algebraically and graphically to determine how many sprockets a company can produce per month given fixed and variable costs. Question 2 involves modeling the areas of a square and circle cut from a piece of wire. Question 3 models revenue based on a demand function relating price and quantity. Question 4 deals with composition of functions relating widget production costs to time.

1. Math 4R Test2A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(1) Linear Models: Solve Algebraically, Check Graphically
Spacely Sprockets Inc. has fixed costs of $10,000 each month
and variable costs of $8.50 per sprocket manufactured. Spacely
Sprockets has $85,000 available to cover these monthly costs. How
many sprockets can Spacely Sprockets produce per month?
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2. Math 4R Test2A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(2) Modeling: Solve Graphically
Four feet of wire is to be cut into two pieces in order to form a square
and a circle.
(2a) Express the sum of the two areas as a function of x, the side of the
square, and r, the radius of the circle.
(2b) Rewrite the sum of the two areas as a function of x alone.
(2c) Graph y = A(x). What domain makes sense in this situation?
(2d) Find the maximum area. For what value of x do you get this max?
(2e) Find the minimum area. For what value of x do you get this min?
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3. Math 4R Test2A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(3) Modeling: Solve Graphically
The price p and the quantity x sold of a certain product obey the
following demand function:
-x
p(x) = 3 + 100, 0 ≤ x ≤ 300
(3a) Express the revenue R in terms of x.
(3b) Find the revenue when 100 units are sold.
(3c) How many units must sell to earn a revenue of $5000.
(3d) Find the maximum revenue.
(3e) What price should you charge per unit to maximize revenue?
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4. Math 4R Test2A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(4) Composition
The weekly cost in $ to manufacture x widgets is given by the function
C(x) = 60x + 750. The number of widgets produced at your factory in t
hours is given by the function x(t) = 50t.
(4a) State and interpret C(x(t)).
(4b) Graph y = C(x(t)).
(4c) Find ∆t such that ∆C = $15000.
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