Question

I currently sell my merchandize at $50 per unit, at which sales price I sell 300 units each month. I intend to put the merchandize on sale and my market research shows that, for each $5 reduction in price, I will sell 25 additional units each month. Express my reduction in sales price as a linear function of my monthly demand (i.e. the number of units sold each month).

Answer 1

$0.4167 per unit.

Explanation:

To express the reduction in sales price as a linear function of the monthly demand, we need to determine the relationship between the number of units sold and the reduction in price. Given that for each $5 reduction in price, an additional 25 units are sold each month, we can use this information to create a linear function. Let's break it down step by step: 1. Start with the initial sales price: $50 per unit. 2. Determine the reduction in price for each additional unit sold: $5 per unit. 3. Calculate the additional units sold for each $5 reduction: 25 units. 4. To find the monthly demand, we need to calculate the total reduction in price, which is equal to the number of additional units sold multiplied by the reduction in price per unit. For example, if we reduce the price by $5, we will sell an additional 25 units, resulting in a total reduction in price of $5 x 25 units = $125. 5. Finally, we can express the reduction in sales price as a linear function of the monthly demand by dividing the total reduction in price by the number of units sold each month. In this case, the linear function would be: (Total reduction in price) / (Number of units sold each month) = $125 / 300 units = $0.4167 per unit. Therefore, the reduction in sales price as a linear function of the monthly demand is approximately $0.4167 per unit.