Modeling for Business: Part One — Test Answers

What is the domain of the graphed function?

What is the domain of the graphed function?

With the addition of a $⁢0.50 per print job expense for binding materials, what is the updated equation to model the total monthly expenses E⁡(q) for the printshop?

What are the break-even points?

Which research question would help in understanding the impact of marketing campaigns on the consumer ratings of the wearable fitness tracker?

If the government sets a price ceiling of $3 in the laptop market after the demand has shifted left due to the rising popularity of tablets, what is the likely impact on the laptop market?

How many units must the store sell to break even?

Given the quadratic function f⁡(x)=2⁢x^2−4⁢x+1 , follow these steps to graph the function: Step 1: Find the vertex of the function. - Identify the vertex (x,y) , locate the coordinate pair, and plot the point in the coordinate plane. Step 2: Find one other point on the graph. - Choose a simple value for x (such as x=0 ). - Substitute this value into the function to find the corresponding y -coordinate. - Identify the point (x,y) Locate the coordinate pair, and plot the point in the coordinate plane.

An ice cream shop generates 80% of its annual revenue during the summer months, resulting in financial difficulties during the winter.

Which graph represents the system of equations? y=x^2−2⁢x−3 y=−2⁢x+6

The price that companies set for a product is determined by market demand. The graph represents the demand, where x represents thousands of units produced. Expand Image Which statement is true about the solution in terms of the situation? Round to the nearest whole number.

Given the expense function E⁡(q)=8+2⁢q , which table correctly represents the relationship between the quantity q and the total expenses E⁡(q) ?

A toy store purchases a toy for $⁢30 and marks it up by 50% During a holiday sale, the store offers a 25% discount on the marked-up price. If 100 toys are sold during the sale, what is the total revenue?

A retail company has $500,000 in cash and $1 million in inventory. The company's sales have been declining, leading to excess inventory. What is the likely impact on the company's financial health?

A coffee shop has fixed monthly expenses of $⁢2,000 and a variable cost of $⁢2 per cup of coffee sold. The revenue is $⁢0 when 0 cups are sold and $⁢0 when 400 cups are sold due to capacity limits. The maximum revenue occurs when 200 cups are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the number of cups of coffee sold?

Given the expense function E⁡(q)=8+2⁢q , which table correctly represents the relationship between the quantity q and the total expenses E⁡(q) ?

An investor wants to know the maximum expected profit for a company’s signature product. The profit formula can be represented using the function P⁡(x)=−15⁢x^2+1,800⁢x+125,000 , where x is the selling price of the product. Use a graphing calculator to determine the maximum expected profits. Round to the nearest cent if necessary. Enter your answer in the box.

Here is a graph of a parabola: Expand Image

A small toy-manufacturing company has the following details: - The cost to produce each toy is $⁢3.00 - The fixed costs are $⁢4.00 - The total expense function is given by E⁡(q)=4+3⁢q , where q is the quantity of toys produced and E⁡(q) is the total expense. Graph the expense function E⁡(q) in terms of the quantity q on the coordinate plane. Click on two points that belong to the function.

A portfolio manager wants to distribute $⁢60,000 between two investments. The risk function is R⁡(x)=0.029⁢x^2−0.018⁢x+0.009 . If x is the portion invested in the first option, how should the manager distribute the funds to minimize risk? Round your answer to the nearest thousandth if necessary.