Question

The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x) = 0.22x. The profit (in millions of dollars) from the sale of x units is given by P(x) = 0.083x -0.7. (a) Find the cost equation. (b) What is the cost of producing 7 units? (c) What is the break-even point? Show all of your work on paper and submit it on canvas. your won't get any credit for the last answer without submission on Canvas (a) C(x) = 0.137x+0.7 (Use integers or decimals for any numbers in the equation.) (b) The cost of producing 7 units is $ 1.7 million. (Type an integer or a decimal.) (c) The break-even point occurs when about 8.4337 units are sold. (Round to the nearest thousandth as needed.)

Answer 1

The cost equation C(x) is 0.137x + 0.7, found by rearranging the profit equation. The cost for producing 7 units is $1.7 million. The break-even point is at approximately 8.4337 units sold.

Step-by-step explanation:

The revenue and profit from the sale of x units at a home supply outlet are represented by two functions: R(x) = 0.22x and P(x) = 0.083x -0.7, respectively. The cost equation C(x) is needed, which can be found by rearranging the profit equation, P(x) = R(x) - C(x), solving for C(x):

• P(x) = R(x) - C(x)
• 0.083x - 0.7 = 0.22x - C(x)
• C(x) = 0.22x - (0.083x - 0.7)
• C(x) = 0.137x + 0.7

The cost of producing 7 units can be found by evaluating C(7):

• C(7) = 0.137(7) + 0.7
• C(7) = 0.959 + 0.7
• C(7) = $1.659 million, which rounds to $1.7 million

To find the break-even point, we set the profit equation equal to zero and solve for x:

• 0 = 0.083x - 0.7
• 0.7 = 0.083x
• x = 0.7 / 0.083
• x ≈ 8.4337

Therefore, the break-even point occurs when approximately 8.4337 units are sold.