Question

[2] Studies conducted by a firm confirmed that the sales volume (V) of its product is relative to its unit selling price (P) and derived an equation to estimate the sales volume, V $100- P If the cost of production is composed of $1000 fixed cost and $10 variable cost per part (a) Draw a graph with the sales volume (V) from 0 to 100 on the x axis, and total cost and total income from $0 to $2500 on the y axis. Plot both the cost and income curves (b) Determine the breakeven point (lowest sales volume where total sales income just equals total production cost). (c) Determine the sales volume (V) at which the firm's profit is a maximum

Answer 1

V= $100 - P

TC = fixed cost + variable cost = $1,000 + $10(V)

TR = P.V

(a). when V= 0,

TR = 0

TC = $1,000 + $10(0) = $1,000

when V = 100

V= $100 - P

P = 0

TR = 0

TC = $1,000 + $10(100) = $2,000

when V=50

P = $50

TR = $50 * 50 = $2500

TC = $1, 000 + $10(50) = $1,500

Below is the graph for total income and total cost with sales volume from 0 to 100 on x-axis and total income and total cost from $0 to $2500 on y-axis.

2500 total cost curve 2000 total income & total cost 1500 1000 500 total revenue curve 50 sales volume

(b). The breakeven point where total cost equals to total revenue is calculated as follows:

TR = TC

P.V = $1,000 + $10(V)

($100 - V)V = $1,000 + $10(V)

V² -90V +1,000 = 0

solving this quadratic equation by using formula x= [-b $\pm$ (b² - 4ac)^1/2]/2a

V = (90 $\pm$ 64)/2 = 77 and 13

Therefore the lowest sales volume for breakeven point is 13.

(c). Firm's profit is maximum where MR = MC

TR = P.V = ($100 - V)V = $100.V - V²

MR = dTR/dV = $100 - 2V

TC = $1,000 + $10.V

MC = dTC/dV = $10

MR=MC

$100 - 2V = $10

V = 45

Sales Volume at which firm's profit is maximum is 45.