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Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 3 pounds, they charge $ 0.75 per pound. For packages weighing between 3 and 18 pounds, they charge $ 2.25 per pound. For packages weighing greater than or equal to 18 pounds, they charge $ 2.5 per pound. IPS refuses to ship any parcel weighing more than 52 pounds. There is also a flat fee of $ 2 for all deliveries and an additional fee of $ 5 for all deliveries weighing 18 pounds or more.Complete the following description of a piecewise function so that is describes the shipping costs C(x)𝐶(𝑥) in dollars as a function of the weight x𝑥 in pounds. Write the individual formulas in order of increasing  x𝑥 .  C(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩    𝐶(𝑥)={        0.75x+2 if x𝑥 is in the interval 2.25x+2 if x𝑥 is in the interval 2.5x+7 if x𝑥 is in the interval

Question

Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 3 pounds, they charge 0.75perpound.Forpackagesweighingbetween3and18pounds,theycharge 0.75 per pound. For packages weighing between 3 and 18 pounds, they charge 2.25 per pound. For packages weighing greater than or equal to 18 pounds, they charge 2.5perpound.IPSrefusestoshipanyparcelweighingmorethan52pounds.Thereisalsoaflatfeeof 2.5 per pound. IPS refuses to ship any parcel weighing more than 52 pounds. There is also a flat fee of 2 for all deliveries and an additional fee of $ 5 for all deliveries weighing 18 pounds or more.Complete the following description of a piecewise function so that is describes the shipping costs C(x)𝐶(𝑥) in dollars as a function of the weight x𝑥 in pounds. Write the individual formulas in order of increasing  x𝑥 .  C(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩    𝐶(𝑥)={        0.75x+2 if x𝑥 is in the interval 2.25x+2 if x𝑥 is in the interval 2.5x+7 if x𝑥 is in the interval

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Solution

The piecewise function for the shipping costs C(x) in dollars as a function of the weight x in pounds can be described as follows:

C(x) = { 0.75x + 2, if 0 < x ≤ 3 2.25x + 2, if 3 < x < 18 2.5x + 7, if 18 ≤ x ≤ 52 }

This means that if the weight of the package is less than or equal to 3 pounds, the cost is 0.75 times the weight plus a flat fee of 2.Iftheweightisbetween3and18pounds,thecostis2.25timestheweightplusaflatfeeof2. If the weight is between 3 and 18 pounds, the cost is 2.25 times the weight plus a flat fee of 2. If the weight is 18 pounds or more (but not more than 52 pounds), the cost is 2.5 times the weight plus a flat fee of 7(whichincludesthe7 (which includes the 2 flat fee and the additional $5 fee for packages weighing 18 pounds or more).

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