A souvenir store charges PHP 15.00 per keychain for the first 50 orders. If the order exceeds to 50 keychain, the store charges PHP 12.50 per keychain for the exceeded orders of keychain. Express the total cost K(x) of the x number of keychain as a function of x.
To express the total cost K(x) of the x number of keychains as a function of x, we need to consider two scenarios:
1. When x is less than or equal to 50:
In this case, each keychain costs PHP 15.00. Therefore, the total cost is given by the product of the number of keychains and the cost per keychain:
K(x) = 15.00 * x
2. When x is more than 50:
The cost for the first 50 keychains remains PHP 15.00 per keychain. However, for the exceeded orders of keychains, the price reduces to PHP 12.50 per keychain. Therefore, the total cost can be expressed as follows:
K(x) = (15.00 * 50) + (12.50 * (x - 50))
To summarize, we can define the total cost function K(x) for the x number of keychains as follows:
K(x) = {
15.00 * x, if x <= 50
(15.00 * 50) + (12.50 * (x - 50)), if x > 50
}