Question $220$ marks ABC electronics is engaged in manufacturing of TVs$,$ Smartphones, and Refrigerators in its factory with $30000$ sq$.$ft$.$ of area. The company wants to retain at least $10$ TVs and $20$ smartphones as a fixed reserve in any month. These quantities can be produced in its factory or bought from another company. After taking care of the reserved quantities, any excess production would be sold. Over the last decade, mean selling prices have been INR $25000$ and INR $18000$ per unit of TVs and smartphones, respectively. The purchase prices are $20\%$ more than the selling prices. Another profitable product is Refrigerator, which company expects to sell at INR $35000$ per unit; however, due to an imposed rule by Government, there is a quota on refrigerator production. Any amount more than the applicable quota can be sold only at INR $20000$ per unit. At present, the limit for this quota is $50$ units. Based on the past experience and requirements of the different product lines, the company knows that the average production capacity in its factory is around $2$ units, $3$ units, and $4$ units per $500$ sq$.$ft$.$ of area for TVs$,$ Smartphones, and Refrigerators product line, respectively. Overall manufacturing cost $($including raw material, labour, etc.$)$ converted in terms of the area $($i$.$e$.,10$ sq$.$ ft$.)$ is INR $7,$ INR $5,$ and IN $9$ per $10$ sq$.$ft$.$ of area for TVs$,$ Smartphones, and Refrigerators product line, respectively. The company wants to decide how much area to devote to each product line a$)$ Formulate a model for this problem. b$)$ The company's average production capacity directly depends on the workers' performance. Considering three scenarios for workers' performance $($i$.$e$.,$ Favourable with $10\%$ above average production capacity, Average, and Unfavourable with $10\%$ below average production capacity$),$ formulate a model for this situation also. You may consider that the three scenarios have an equal probability.