Let's break down the problem step-by-step to determine the cost to ship 2,000 lbs of goods for a distance of 700 miles with a 20% premium for 3-5 day shipping.
### Step 1: Determine the Price Bracket
From the given distance-price table:
- Distance (miles):
- 0-200: \[tex]$100 per 100 lbs
- 201-400: \$[/tex]120 per 100 lbs
- 401-600: \[tex]$200 per 100 lbs
- 601-800: \$[/tex]240 per 100 lbs
- 801-1000: \[tex]$400 per 100 lbs
Since the shipping distance is 700 miles, it falls within the range of 601-800 miles. Therefore, the price per 100 lbs for this distance bracket is \$[/tex]240.
### Step 2: Calculate the Base Cost
Now, we need to calculate the base cost to ship 2,000 lbs at the rate of \[tex]$240 per 100 lbs.
First, determine how many sets of 100 lbs are there in 2,000 lbs:
\[ \text{Number of 100 lbs sets} = \frac{2000 \text{ lbs}}{100 \text{ lbs}} = 20 \]
Next, calculate the base cost:
\[ \text{Base Cost} = \text{Number of 100 lbs sets} \times \text{Price per 100 lbs} \]
\[ \text{Base Cost} = 20 \times 240 = \$[/tex]4800 \]
### Step 3: Calculate the Total Cost Including Premium
The premium for 3-5 day shipping is 20%. To find the total cost including the premium, we need to add 20% to the base cost:
[tex]\[ \text{Premium Cost} = \text{Base Cost} \times (1 + \text{Premium Rate}) \][/tex]
[tex]\[ \text{Premium Cost} = \$4800 \times (1 + 0.20) \][/tex]
[tex]\[ \text{Premium Cost} = \$4800 \times 1.20 = \$5760 \][/tex]
Therefore, the total cost to ship 2,000 lbs of goods from Chicago to Atlanta (700 miles) using 3-5 day shipping is \$5760.
