(a) Type of Operations Research Problem:

The problem described is a Linear Programming Problem (LPP), which aims to optimize (maximize) returns on inventory investments under given constraints. (2 Marks)

(b) Mathematical Formulation:

Let:

• $C$: Investment in conservative inventory (in naira)
• $S$: Investment in speculative inventory (in naira)

(i) Objective Function:

The objective is to maximize the total return on investments in both conservative and speculative inventories.

Maximize Z=1.6C+2.0S

Where:

• 1.6C : Return on investment in conservative inventory
• 2.0S2 : Return on investment in speculative inventory

(4 Marks)

(ii) Constraint Inequalities:

The constraints can be formulated as follows:

1. Total Investment Constraint:

   C+S  ≤  100,000The total investment should not exceed N100,000.

2. Conservative Investment Constraint:

   C  ≤  80,000 The investment in conservative inventory should be at most N80,000.

3. Speculative Investment Constraint:

   S  ≥  12,000The investment in speculative inventory should be at least N12,000.

   1. Monetary Policy Regulation:

      The investment in speculative inventory should be at most one-third of the investment in conservative inventory.

   2. Non-negativity Constraints:

      C  ≥  0, S  ≥  0(8 Marks)

      (iii) Investment Problem:

      The investment problem is to determine the values of C and S that maximize the total return (Z), subject to the above constraints. Mathematically:

      Maximize Z  =  1.6C  +  2.0S

C+S  ≤  100,000 (available fund constraint)
C ≤ 80,000  (Conservative investment policy constraint
C ≥ 12,000  (Speculative investment policy
C ≤ 1/3 x (monetary policy constraint)

Non negativity/hidden constraint C,S ≥ 0