Questions: A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x)=R(x) is called the break-even point. Assume that the below table can be expressed as a linear function. Find (a) the cost function, (b) the revenue function, and (c) the profit function. (d) Find the break-even point and decide whether the product should be produced, given the restrictions on sales. Fixed cost Variable cost Price of item 150 20 25 According to the restriction, no more than 26 units can be sold. (a) The cost function is C(x)= (Simplify your answer.)

A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x)=R(x) is called the break-even point. Assume that the below table can be expressed as a linear function. Find (a) the cost function, (b) the revenue function, and (c) the profit function. (d) Find the break-even point and decide whether the product should be produced, given the restrictions on sales. Fixed cost Variable cost Price of item 150 20 25 According to the restriction, no more than 26 units can be sold. (a) The cost function is C(x)= (Simplify your answer.)
Transcript text: Part 1 of 4 Points: 0 of 1 Save A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of $x$ (the number of items produced and sold) where $C(x)=R(x)$ is called the break-even point. Assume that the below table can be expressed as a linear function. Find (a) the cost function, (b) the revenue function, and (c) the profit function. (d) Find the break-even point and decide whether the product should be produced, given the restrictions on sales. \begin{tabular}{|c|c|c|} \hline Fixed cost & Variable cost & Price of item \\ \hline$\$ 150$ & $\$ 20$ & $\$ 25$ \\ \hline \end{tabular} According to the restriction, no more than 26 units can be sold. (a) The cost function is $C(x)=$ $\qquad$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Cost Function

The cost function is given by \(C(x) = 150 + 20x\).

Step 2: Revenue Function

The revenue function is given by \(R(x) = 25x\).

Step 3: Profit Function

The profit function is given by \(P(x) = 25x - (150 + 20x) = 5x - 150\).

Step 4: Break-even Point

The break-even point is found by solving \(C(x) = R(x)\), which gives \(x = \frac{150}{5}\). Thus, the break-even point is at \(x = 30\) units.

Step 5: Decision on Production

Given the restrictions on sales (\(S = 26\)), the product should not produce since the break-even point is greater than the sales restriction.

Final Answer:

The cost, revenue, and profit functions are defined as above with a break-even point at 30 units. Based on the given restrictions, the firm should not produce the product.

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