### State three components governing a linear programming model

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QUESTION 1

A company produces two types of calculators, namely: scientific and graphing calculators. Long-term projections indicate an expected daily demand of at least 100 scientific and 80 graphing calculators. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be manufactured daily. In order to satisfy a shipping contract, at least 200 calculators much be shipped each day. If each scientific calculator sold results in Rs 2 loss, and each graphing calculator produces a Rs 5 profit. How many of each type should be made daily to maximise net profits?

(a) State three components governing a Linear Programming Model

(b) Formulate the complete linear programming model for the above problem defining carefully all the components

(c) Using graph paper, plot the constraints lines for this linear programming problem and indicate clearly the feasible region, R

(d) Determine

(i) the feasible corner point (X)

(ii) the number of each type of calculator the company should produce in order to maximise the profit

(iii) Thus evaluate that profit

(e) List the limitations of Linear Programming?

QUESTION 2

(a) (i) Define inventory and outline the purpose of inventory management

(ii) Outline the different costs associated with inventory

(b) At Antara Bookshop, the demand for guide books is 1,200 per year. The books are purchased from a Supplier for Rs9 each. Order costs are Rs10 per order. The annual cost of carrying stock is Rs2.50 per unit. Assume that there are 250 working days in the year

(i) Outline the assumptions that must be satisfied for the economic order quantity model

(ii) Calculate the EOQ

(iii) Find the number of orders that should be placed each year

(iv) Evaluate the time between orders

(v) Calculate the total annual cost

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