A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, and so on) of $56,000 per day and variable costs (labor, materials, and so on) of $1,600 per unit produced. The mowers are sold for $2,000 each. The costs and rev

(A) To break even, the revenue generated from selling riding lawn mowers should be equal to the total cost incurred in manufacturing them. So, we can set the revenue equation equal to the cost equation: $2,000x = 56,000 + 1,600x Simplifying and solving for x: $400x = $56,000 x = 140 Therefore, the company needs to manufacture and sell 140 riding lawn mowers each day to break even. (B) We can graph both equations on the same coordinate system, with the total cost on the y-axis and the number of mowers produced and sold on the x-axis. The break-even point is where the two lines intersect. The equation for the cost line is y = 56,000 + 1,600x, and the equation for the revenue line is y = 2,000x. The graph would show a diagonal line representing revenue (starting at the origin with a slope of 2,000) and a horizontal line representing cost (at a height of 56,000 on the y-axis). The break-even point occurs where these two lines intersect, at the point (140, 280,000). (i) The region between the cost line and the revenue line to the left of the break-even point represents a loss for the company. This is because the cost of producing and selling the mowers is greater than the revenue generated from selling them. (ii) The region between the cost line and the revenue line to the right of the break-even point represents a profit for the company. This is because the revenue generated from selling the mowers is greater than the cost of producing and selling them.