Example 2-1. The demand: 50,000 yd³ of mixed-asphalt-paving material during four months (17 weeks of 5 days/week)

Cost Factor	Site A	Site B
Average hauling distance	4 miles	3 miles
Monthly rental of the site	$2,000	$7,000
Cost to set up and remove equipment	$15,000	$50,000
Hauling expense	$2.75/yd3-mile	$2.75/yd3-mile
Flagperson	Not required	$150/day

Questions:

1. Which site has the lowest total cost?
2. For the site chosen, when will the contractor start having a breakeven (e.g. after delivering a certain amount of material)?
3. What would be the breakeven amount for the unit price equals to $15, $11.5, and $10?

Solution

You are encouraged to replicate the approach presented here to solve the question. As we discussed in class, write down every detail will help you think and prevent unintentional mistake.

Part 1. Total cost = Fixed cost + Variable cost

For site A,

Variable cost (hauling cost) = unit produced * unit cost = ____________________,. yd³ * ( _____________________ miles * $ _____________________ / yd³-mile) = $ _____________________ . Do replace the comma symble of thousands with a space, e.g. "10 000" instead of "10,000".

Fixed cost = rent + setup + flagperson = $ _____________________ /month * _____________________ months + $ _____________________ + $ ___________________ = $ _____________________

So site As total cost = $ _____________________

In the same token, for site B,

Variable cost = _____________________ yd³ * ( _____________________ * $ _____________________ /yd³-mile ) = $ _____________________

Fixed cost = rent + setup + flagperson = $ _____________________ /month * _____________________. months + $ _____________________ + $ _____________________ /day * _____________________ days/week * _____________________ weeks = $ _____________________ + $ _____________________+ $ ______________________ = $ _____________________

So site Bs total cost = $ _____________________ <= The contractor will chose site B due to its lower cost.

Question 2 of 3

What follows is a fill in the blank question with 10 blanks.

Part 2. Now we need to find the breakeven point. As we discussed in class, the contractor will spend 4 months to deliver everything. So we are in fact looking for a specific amount of material to be delivered when the contractors revenue equals the total cost of delivering that amount of material.

The textbook states that the contractor will sell the material for $12/yd3.

Assuming an amount of material, Y yd³, will need to be delivered in order to have a breakeven, then the total cost at that point of time is

Fixed cost = $ _____________________ for site B, which is not going to change due to the amount being delivered.

Variable cost = unit produced * unit cost = Y yd³ * ( _____________________miles * $ _____________________ /yd³-mile ) = $ _____________________ * Y

The revenue at that point = unit sold * unit price = Y yd³ * $ _____________________ /yd³ = $ _____________________ * Y

To have a breakeven, the revenue has to equal to the total cost, so

$ _____________________ * Y = fixed cost + variable cost = $ _____________________ + $ _____________________ * Y

So the amount of material to be delivered, Y = _____________________ yd³

Question 3 of 3

What follows is a fill in the blank question with 3 blanks.

Part 3. The same equation, revenue = total cost, can be used here. The only thing changed is the unit price.

For unit price = $15 /yd³, the amount of material to be delivered, Y = _____________________yd³ (write down your answer as an integer, e.g. no decimal points)

Do note that you might have tried to round off the answer. However, that answer is not correct as it is not enough to reach the breakeven point (the shaded area in the right-hand side).

In the same token, for unit price = $11.5 /yd³, the amount of material to be delivered, Y = _____________________ yd³ (write down your answer as an integer).

For unit price = $10 /yd3, the amount of material to be delivered, Y = _____________________ yd³ (write down your answer as an integer).

Do note that the total amount to be delivered is 50,000 yd³ within four months, which is less than your amount above. What this means is that the two lines just convert too slowly, way behind the total amount required. It also means that the unit price is not enough to cover everything; the contractor will lose money at the end.