Question

The Candy Factory sells candy by the​ pound, charging ​$1.25 per pound for quantities up to and including 25 pounds. Above 25 ​pounds, the Candy Factory charges ​$1.20 per pound for the entire quantity. If x represents the number of​ pounds, the price function is as follows. ​p(x)equalsStartSet Start 2 By 2 Matrix 1st Row 1st Column 1.25 x 2nd Column for x less than or equals 25 2nd Row 1st Column 1.20 x 2nd Column for x greater than 25 EndMatrix Find ModifyingBelow lim With x right arrow 25 Superscript minus p (x )​, ModifyingBelow lim With x right arrow 25 Superscript plus p (x )​, and ModifyingBelow lim With x right arrow 25 p (x ).

Answer 1

a) 31.25

b) 30

Explanation:

The price function is given as:

`\mathbf{P(x) =\left \{ {1.25x \ for \ x \ \leq \ 25} \atop {1.20x \ for \ x \ > \ 25}} \right. }`

Find:

`\mathbf{ \lim_(x \to 25^-) P_((x))}`

`\mathbf{ \lim_(x \to 25^+) P_((x))}`

`\mathbf{P(x) =\left \{ {1.25x \ for \ x \ \leq \ 25} \atop {1.20x \ for \ x \ > \ 25}} \right. }`

`\mathbf{ \lim_(x \to 25^-) P_((x)) = 1.25 * 25} \\ \\ =31.25`

`\mathbf{ \lim_(x \to 25^+) P_((x)) = 1.20 * 25} \\ \\ =30`