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A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.

A bakery makes and sells hot cocoa bombs during the holidays The first 12 hot cocoa bombs of an order cost is 400 each Each of the next 6 hot cocoa bombs cost 3 class=

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Solution

Step 1

Given data for C(x), the bakery's pricing

[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]

Required

Step 1

To find the cost of 8 hot cocoa bombs

[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]

Step 2

To find the cost of 18 hot cocoa bombs

[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3

To find the C(30)

[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]

Step 4

What C(30) represents.

C(30) represents the cost of ordering 30 hot cocoa bombs which is $105

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