15. A company wants to plan production for the ensuing year so as to minimise the combined cost of production and inventory storage costs. In each quarter of the year, demand is anticipated to be 65, 80, 135 and 75 respectively. The product can be manufactured during regular time at a cost of Rs 16 per unit produced, or during overtime at a cost of Rs 20 per unit. The table given below gives data pertinent to production capacities. The cost of carrying one unit in inventory per quarter is Rs 2. The inventory level at the beginning of the first quarter is zero.

Formulate the given problem to minimise the production plus storage costs for the year.

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Capacities (units) Quarter Regular time Overtime Quarterly demand 1234 80 10 65 90 10 80 95 20 135 70 10 75