0000:00:00:00:00Start8Number 8ExplanationThe cost function for a product is given by B(x)=360+40x+0.1x2B(x) = 360 + 40x + 0.1x^2B(x)=360+40x+0.1x2 and the revenue function is given by P(x)=60xP(x) = 60xP(x)=60x, where xxx is the number of product units. The break-even point will occur when the number of products is... Units.180180180 and 202020180180180 and 101010170170170 and 151515170170170 and 202020160160160 and 252525ExplanationConcept of Break-Even Point The Break-Even Point is the condition where there is neither profit nor loss, meaning total revenue equals total cost. B(x)=P(x)B(x) = P(x)B(x)=P(x) Solving the Equation Substitute the given functions: 360+40x+0.1x2=60x360 + 40x + 0.1x^2 = 60x360+40x+0.1x2=60x0.1x2−20x+360=00.1x^2 - 20x + 360 = 00.1x2−20x+360=0 To make calculation easier, multiply both sides by 101010: x2−200x+3600=0x^2 - 200x + 3600 = 0x2−200x+3600=0 Determining the Value of x We use quadratic factorization. We look for two numbers that multiply to 360036003600 and add up to −200-200−200. These numbers are −180-180−180 and −20-20−20. (x−180)(x−20)=0(x - 180)(x - 20) = 0(x−180)(x−20)=0 The roots are: x1=180orx2=20x_1 = 180 \quad \text{or} \quad x_2 = 20x1=180orx2=20 Thus, the break-even point occurs when the number of products is 180180180 units and 202020 units.
8Number 8ExplanationThe cost function for a product is given by B(x)=360+40x+0.1x2B(x) = 360 + 40x + 0.1x^2B(x)=360+40x+0.1x2 and the revenue function is given by P(x)=60xP(x) = 60xP(x)=60x, where xxx is the number of product units. The break-even point will occur when the number of products is... Units.180180180 and 202020180180180 and 101010170170170 and 151515170170170 and 202020160160160 and 252525ExplanationConcept of Break-Even Point The Break-Even Point is the condition where there is neither profit nor loss, meaning total revenue equals total cost. B(x)=P(x)B(x) = P(x)B(x)=P(x) Solving the Equation Substitute the given functions: 360+40x+0.1x2=60x360 + 40x + 0.1x^2 = 60x360+40x+0.1x2=60x0.1x2−20x+360=00.1x^2 - 20x + 360 = 00.1x2−20x+360=0 To make calculation easier, multiply both sides by 101010: x2−200x+3600=0x^2 - 200x + 3600 = 0x2−200x+3600=0 Determining the Value of x We use quadratic factorization. We look for two numbers that multiply to 360036003600 and add up to −200-200−200. These numbers are −180-180−180 and −20-20−20. (x−180)(x−20)=0(x - 180)(x - 20) = 0(x−180)(x−20)=0 The roots are: x1=180orx2=20x_1 = 180 \quad \text{or} \quad x_2 = 20x1=180orx2=20 Thus, the break-even point occurs when the number of products is 180180180 units and 202020 units.
