Question

A new shop wants to sell Muffins, the sell price is 2.5 dollars per unit. The cost for production is 1 dollar per unit. At the first day, they made 2000 units, however, they overestimated the demand, so they had to resell the rest to other shops 0. 5 per muffin, under this condition, the first day’s profit was at breakeven point. The second day, the boss changed the number of productions based on the first day’s sale.And plan to set "buy one get a free one" strategy to attract customers. Since the muffins’ good taste, a lot of customers came back to buy muffins again and brought their friends asnew customers, so 100 of the customers did not get the muffins, per muffins loss is 2 dollars. The second day’s profit is 400 dollars. How many changes on the two day’ production?g

Answer 1

The price went from 2.50 dollar per unit to 1.25

Answer 2

The price went from 2.50 dollar per unit to 1.25

And quantity sold of first hand muffin increase from 500 to 1,600

Step-by-step explanation:

First day:

We build the equation and solve considering:

a= first hand muffin sold at 2.5 dollar

b = left-over sold at 0.5 dollar

considering the shop made 2,000 muffin and the cost is 1 dollar per muffin:

quantities equation: a + b = 2,000

price equation: 2.5a + 0.5b = 2,000

2.5(2,000 - b) + 0.5b = 2,000

5,000 - 2.5b + 0.5b = 2,000

3,000/2 = b = 1,500

a = 2,000 - b = 2,000 - 1,500 = 500

It sale 500 dollar of muffin at 2.5 and 1,500 at 0.5 getting a total of 2,000 revenue to cover the cost.

Second day:

There is a decrease in price to 1.25 per muffin

This generates a profit of 400 dollar thus:

(sales price less cost) x quantity = profit

(1.25 - 1) x a = 400

a = 400/0.25 = 1,600