Question

Brown Oil Company transports gasoline to its distributors by truck.  The company recently contracted to supply gasoline distributors in southern Ohio,

and it has $1,600,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks (e.g. capital expenditures).   Three models of gasoline tank trucks are available:

Truck Model

Monthly Truck Capacity (Gallons)

Purchase Cost

Monthly Operating Cost, including Depreciation

Sub 100

75000

$200,000

$1,550

Oiler J

62500

$160,000

$1,425

Texan

30000

$100,000

$1,350

The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline.  Because of the size and speed differences of the trucks, the monthly capacity of the trucks will vary.

The company wants to meet customer demand and minimize monthly operating costs.

a.        How many of each type of truck will the company buy?  What is the total capital expenditure?  What is the expected monthly operating cost?

b.  In the answer tab, type out the objective function and constraints for part a.

c.  Management has asked that two additional considerations be made.  The company must purchase at least 3 Texans, and no more than half of the new models may be Sub 100.

What is the optimal solution (number of each truck) and the objective function value with these additional considerations?

Answer 1

Let S denotes number of Sub 100 company buys, O denotes number of Oiler J company buys and T denotes number of Texan company buys.

Objective Function:

Min: z= 1550 *S + 1425*O + 1350*T

Constraints:

Monthly demand = 550,000 gallons of gasoline

So,

(as monthly demand need to satisfy completely)

Amount for expansion = $1,600,000

So, total purchse cost must be less than $1,600,000.

Thus,

Using excel solver:

(a) each type of truck will the company buy

Sub 100 = 7

Oiler J = 0

Texan = 0

Total capital expenditure = $1,400,000

Expected monthly operating cost = $10,850

(values are different from the one in solver because we cant buy 7.33 sub 100 so we need to consider integer value of it)

(b) Problem:

Min: z= 1550 *S + 1425*O + 1350*T

subject to:

(c) additional constraints:

purchase at least 3 Texans:

no more than half of the new models may be Sub 100:

For integer solution: number of each truck :

Sub 100 = 4

Oiler J =2

Texan = 3

Optimal Solution =