Modeling for Business — Test Answers

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?

XYZ Corporation has reported a net profit of $⁢200,000 for the fiscal year. The corporation decides to distribute $⁢30,000 in dividends to its shareholders. Based on the net profit and dividend distribution, determine the amount subject to corporate taxes.

Given the profit function P⁡(x)=−2⁢x^2+8⁢x−3 , graph the function and identify the graph that correctly represents the profit based on the number of units sold. The vertex indicates the maximum profit.

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 business owner is trying to determine the break-even point. The owner uses the revenue function R⁡(x)=−0.014⁢x^2+7,000⁢x , and the cost function is C⁡(x)=180,000+2,000⁢x In both functions, x represents the number of units sold. How many units does the owner need to sell to break even? Round to the nearest whole number if necessary.

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?

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 profit function P⁡(x)=−2⁢x^2+8⁢x−3 , graph the function and identify the graph that correctly represents the profit based on the number of units sold. The vertex indicates the maximum profit.

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

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.

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.

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

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 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?

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.

Here is a graph of a parabola: Expand Image

A business owner is trying to determine the break-even point. The owner uses the revenue function R⁡(x)=−0.014⁢x^2+7,000⁢x , and the cost function is C⁡(x)=180,000+2,000⁢x In both functions, x represents the number of units sold. How many units does the owner need to sell to break even? Round to the nearest whole number if necessary.

A hardware store purchases a drill for $⁢80 and marks it up by 60% They then offer a 20% discount on the marked-up price. The store manager calculates the final sale price as $⁢64 The manager's steps are shown below: Calculate the marked-up price: $⁢80+($⁢80⋅0.60)=$⁢128 Apply the discount: $⁢128−($⁢128⋅0.50)=$⁢64 Identify the mistake in the manager's calculation.

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 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.