Question

The Company has a contract to produce 15,500 batteries for an electric company. The company has four different machines that can produce this kind of battery. Each machine requires a separate setup. The following table shows the specifications of these machines.

Machine	Fixed cost for setup	Variable cost per battery produced	Production Capacity
1	$1200	$2	6000
2	$950	$1.2	3000
3	$1100	$1.9	4500
4	$1350	$2.3	8000

The company cannot use both machines 2 and 3. If machine 4 is used, machine 1 must also be used. Determine the number of batteries that will be produced in each machine to meet the obligations of the contract with the minimum cost possible. Assume that only integer number of batteries can be produced. a) Define the variables. b) Write the mathematical formulation of the problem

Answer 1

a) The variables are

Batteries produced by machine 1 : x₁

Batteries produced by machine 2 : x₂

Batteries produced by machine 3 : x₃

Batteries produced by machine 4 : x₄

b) Mathematical formulation

conditions

6000 x₁ + 4500 x₃ + 8000 x₄ >= 15500

6000 x₁ + 3000 x₂ + 8000 x₄ >= 15500

x₁ , x₂ , x₃ & x₄ are integers i.e, 0, 1 ,2,3 ........N

Minimize ( two cost functions)

Z1 = $ 1200 + $950 + $1350 + $2 x₁ + $1.2 x₂ + $2.3 x₄

Z2 =   $ 1200 + $1100 + $1350 + $2 x₁ + $1.9 x₃ + $2.3 x₄

First minimize Z1 & Z2 and then choose which is minimum of two cost function.