The Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and including 20 pounds. Above 20 pounds, the Candy Factory charges $1.30 per pound for the entire quantity, plus a quantity surcharge k. If x represents the number of pounds, the price function is p(x) = {1.60x for x lessthanorequalto 20, 1.30x + k for x > 20. Find k such that the price function p is continuous at x =20. Explain why it is preferable to have continuity at x =20. The price function p is continuous at x = 20 when k = (Type an integer or a decimal.)

The correct statement is that the real value of k is calculated as 6 given that the price function is continuous and the value of x is 20. This value will give optimum utilization of capital employed by the factory.

The calculation of k when x is either greater than the value of 20 and the similar value of k when the value of x is less than or equal to 20 is given as below.

Hence, the correct statements is that the value of k is 6 when the price function is continuous at x=20 and the factory will benefit using this pricing method so as to achieve optimum utilization sources.

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Step-by-step explanation:

We have been given that the Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and including 20 pounds. Above 20 pounds, the Candy Factory charges $1.30 per pound for the entire quantity, plus a quantity surcharge k.

For the price function be to continuous at , the value of both functions at must be equal. Because a function is continuous if the right hand limit is equal to left hand limit.

Let us solve for k.

Therefore, the price function p is continuous at  , when k is equal to 6.