Blue Split sells ice cream cones in a variety of flavours. The following are data for a recent week: Revenue (1,000 cones at $1.85 each) $1,850 Cost of ingredients $660 Rent 540 Store attendant 640 1,840 Pretax income $10 The manager estimates that if she were to increase the price of cones from $1.85 to $2.02 each, weekly volume would be cut to 850 cones due to competition from other nearby ice cream shops. Estimate the profit-maximizing price per cone.

$1.40

Explanation:

Per cent change in price = ($2.02– $1.85)/$1.85 = +9%

Per cent change in demand = (1000 – 850)/1000 = –15%

The elasticity is = ln(1 + per cent change in quantity sold)/ln(1 + per cent change in price)

= ln(1 – 0.15)/ln(1 + 0.09)

= –0.16252/0.08618

= –1.886

Variable cost = $660/1000

Profit-maximising price = [–1.886/(–1.886+1)]*$0.66 = $1.40

Results are below.

Explanation:

a) To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 75,000 / 4

Break-even point in units= 18,750

b)To calculate the break-even point in dollars, we need to use the following formula:

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 75,000 / (4/10)

Break-even point (dollars)= $187,500

c) Desired profit= $40,000

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units= (75,000 + 40,000) / 4

Break-even point in units= 28,750

d) Desired profit= $35,000

Break-even point (dollars)= (fixed costs + desired profit) / contribution margin ratio

Break-even point (dollars)= (75,000 + 35,000) / 0.4

Break-even point (dollars)= $275,000

e) Desired profit (before taxes)= 25,000/0.7= $35,714

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units=  110,714/4

Break-even point in units= 27,679

Break-even point (dollars)= (fixed costs + desired profit) / contribution margin ratio

Break-even point (dollars)= 110,714/0.4

Break-even point (dollars)=$276,785