What are the decision variables, contraints and objective function for this LPP

Question

I'm starting to learn LP and I am unable to solve this effectively. Can someone please help derive the decision variables, constraints and objective function for this problem so I can solve it?



Each machine costs $1500 per quarter and needs to be used for at least 2 quarters.

Each machine can make 1000 tyres per month.

The demand is 32000 for quarter 1,

46000 for quarter 2,

80000 for quarter 3,

and 16600 for quarter 4.

Inventory costs $5 per quarter per tyre, and inventory must be empty at the end of quarter 4.

Answer 1

Decision variables: the number of machines available and the demand for tyres. Decision variables are Xij, with i representing the number of machines bought t a specific quarter and the number of quarters that the machine has been used. Constraints; the number of machines, their production capacities, and the number of quarters each machine should be used. Objective function; minimize inventory costs and maximize production of tyres. Maximizing profit is the objective function +

OR

Decision variables:

The decision variables are Xij, where i represents the number of machines bought in quarter i (at least 2 quarters) and j represents the number of machines for the remaining two quarters.

Objective function:

We need to specify a criterion for evaluation—an objective function. The most appropriate objective function is to maximize monthly profit. The profit earned is a direct function of the amount of each machine i.e. the decision variables. Monthly profit, designated as z, is written as follows:

z (profit per tyre) * (number of tyres made and sold monthly).

Constraints:

We want to maximize z, but subject to satisfying the stated constraints. To solve the problem, we express these constraints as mathematical equalities or inequalities. The demand for quarters 1 and 2 (represented by i) and demand for quarters 3 and 4 (represented by j) have limits, where j≥i