Linear equation help

Question

Hi,

I'm struggling with this question. I've finished all the subsections besides subsection (d.) Is that section asking for the intersection point of the cost and profit axis? Can anyone post a full solution for this?

Question

Auto-time, a manufacturer of 24-hour variable timers, has a monthly fixed cost of RM48,000 and a production cost of RM8 for each timer manufactured. The units sell for RM14 each.

(a) Sketch the graphs of the cost function and the revenue function, and hence find the break-even point graphically.

(b) Find the break-even point algebraically.

(c) Sketch the graph of the profit function.

(d) At what point does the graph of the profit function cross the x-axis? Interpret your result.

Answer 1

Let x be the number of timers produced and sold.

Cost = 8x + 48,000

Revenue = 14x

Both graph as straight lines. Break-even point is where they intersect. To find the break-even point algebraically, set Revenue = Cost and solve for x.

Profit = Revenue - Cost = 14x - (8x + 48,000) = 6x - 48,000

Profit graphs as a straight line as well. It crosses the x-axis when Profit = 0. Set Profit = 0 and solve for x. It is also the break-even point.