A shipping company is buying new trucks

Question

A shipping company is buying new trucks. The high-capacity trucks cost $50,000 and hold 320 cases of merchandise. The low-capacity trucks cost $30,000 and hold 200 cases of merchandise. The company has budgeted $1,080,000 for the new trucks and has a maximum of 30 people qualified to drive the trucks (1 driver per truck). Due to availability limitations, the company can purchase at most 15 high-capacity trucks. How many of each type of truck should the company purchase to maximize the number of cases of merchandise that can be shipped simultaneously? What is the maximum number of cases that can be shipped simultaneously?

Answer 1

We can look at this either by specifying the number of small trucks, or the number of big trucks.  I am going to specify the number of high-capacity trucks, which I am going to label 'h'.

 

Now I am going to express the number of possible low-capacity trucks (l) in terms of the number of high-capacity trucks (h), forming two different equations, one in terms of cost, and the other in terms of available drivers.

 

My two equations are:

equation 1 (drivers)               l<=30-h

equation 2 (cost)                   l<=(108-5h)/3

 

I then need to determine all possible values of these two equations for up to 15 high-capacity trucks (h<=15), but only take the integer portions of my answers since I can't have fractions of a truck.

 

Using Excel, if I put the number of high-capacity trucks in column A, I would use this formula:

=MIN(INT((108-5*A1)/3),30-A1)

and then copy it down for 15 lines as I changed A1=1 to A15=15.

 

I would then use the formula Total load = 320h+200l to calculate the total load for each of these scenarios.

In Excel this would look like =320*A1+200*B1,  copied down for 15 lines.

 

I could then either find my maximum value of Total load, or generate a graph, which would show that my best scenario would be 9 large trucks, and 21 small trucks, with a total load of 7,080 cases of merchandise.