4. Un distribuidor adquiere balones de gas a un costo de 4 dólares la unidad. Cuando el precio de venta es de 10 dólares se venden 4000 unidades en un mes. Se quiere subir los precios y se estima que por cada aumento de 1dólar en el precio se venderán 200 balones menos. ¿Qué precio se deberá fijar con el fin de obtener una utilidad de 24 000 dólares?

A total profit of $24000 when the price increase per unit is $0 or $14.

That is, a selling price of $10 per unit or $24 per unit will lead to a total profit of $24000.

Step-by-step explanation:

English Translation

A distributor purchases gas canisters at a cost of $4 per unit. When the sale price is $10, 4,000 units are sold per month. Prices are to be raised and it is estimated that for each $ 1 increase in the price, they will be sold. 200 balls less. Determine: What price should be set with the gin to obtain a total profit of $ 24,000?

Solution

Normally, profit is given as (Revenue) - (Cost Price)

When 4000 units are bought at $4 and sold for $10,

Revenue = 10 × 4000 = $40,000

Cost Price = 4 × 4000 = $16,000

Profit = 40,000 - 16,000 = $24,000

For every $1 rise in Price, 200 less units are sold.

Of there's an increase in Price of $x,

Cost Price = 4 × (4000 - 200x) = (16000 - 800x)

Revenue = (10 + x) × (4000 - 200x) = 40000 - 2000x + 4000x - 200x² = (40000 + 2000x - 200x²)

Profit = (Revenue) - (Cost Price)

Profit = (40000 + 2000x - 200x²) - (16000 - 800x) = 40000 + 2000x - 200x² - 16000 + 800x = (24000 + 2800x - 200x²)

What price should be set to obtain a profit of $24000?

Profit = 24000 = 24000 + 2800x - 200x²

2800x - 200x² = 0

x(2800 - 200x) = 0

x = 0 or (2800 - 200x) = 0

x = 0 or x = 14

This means a total profit of $24000 when the price increase per unit is $0 or $14.

That is, a selling price of $10 per unit or $24 per unit will lead to a total profit of $24000.

Hope this Helps!!!