A shipping company sets its charges by applying the following rule; • A fixed cost of K170.50 is charged for cargo handling.
• A charge of K12.50 is added for every kilometre of the length of the journey covered in transporting the cargo to its final destination.
• A variable charge is added to cover tracking and insurance. This charge is K85.00 for ports less than 100km apart, K115.00 for ports between 100km and 500km inclusive and K150.00 for ports over 500km apart.
Let = cost of transporting cargo between two ports and = distance between the ports
a) Construct a multiple formula for this function.
b) Use your formula from part a) to calculate the cost of transporting cargo between two ports that are the following distances apart;
i) 153km ii) 791km
c) If ones cost of shipping cargo (minus the variable charge of tracking and insurance) between two ports is K2300, what is the distance between the two ports. (Note: Give your answer rounded off to the nearest kilometre
Answers
Define x and y:
Let x be the number of km traveled
Let y be the variable charge to cover tracking and insurance.
Define each term:
Fixed Cost = K170.50
Distance Charge = K12.50x
Variable Charge = y where:
y = K85 for x < 100
y = K115 for 100 ≤ x ≤ 500
y = K150 for x > 500
a) Construct the formula:
Total cost = 170.50 + 12.5x + y
where x = number of km traveled
y = K85 for x < 100
y = K115 for 100 ≤ x ≤ 500
y = K150 for x > 500
b) i) The distance is 153 km
Total cost = 170.50 + 12.5x + y
Total cost = 170.50 + 12.5 (153) + 115
Total cost = K2198
b ii) The distance is 791 km
Total cost = 170.50 + 12.5x + y
Total cost = 170.50 + 12.5 (791) + 150
Total cost = K10208
c) Cost of shipping without y is K2300
170.50 + 12.5x = 2300
12.5x = 2300 - 170.50
12.5x = 2129.50
x = 170.36
x ≈ 170 km
Total distance = 170 km