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2 years ago

Your part time job pays you $14/h. You work approximately 12 hours/week.

Mathematics

1 answer:

kirill115 [55]2 years ago

4 0

Answer:

BOX 1 = 672.00

(14 * 12 = 168

168 * 4 = $ 672 )

2. BOX 2 = 282.95

(Cell phone= $45 A MONTH

Eating outside = $50 A MONTH

12 .50 * 4 = 50 (4 WEEKS A MONTH )

Transportation = 131.2 A MONTH

32.80 * 4 = 131.2 (4 WEEKS A MONTH )

Movie = $16.75 A MONTH

Charity = $ 40 A MONTH

10 * 4 (4 WEEKS A MONTH )

 MONTHLY EXPENSE  = 45 + 50 + 131.2 + 16.75 + 40

 MONTHLY EXPENSE  = 282.95 )

3. BOX 3 = 389.05

Money that can be saved = Monthly income - Monthly expense

Money that can be saved = 672 - 282.95

= 389.05

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$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

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$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

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$Volume = LWH$

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Substitute $L = 2W$

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Make H the subject

$H = \frac{128}{2W^2}$

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The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

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$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

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