23. A small metal press shop makes Ash Trays and Tea Trays. The process consists ofbuying sheet metal from the market, cutting out appropriate pieces for ash tray /tea tray on stamping machines, forming the stamped pieces into ash tray/tea tray and finally painting in the Spray Painting Booth. The finished products are sold through a distributor who is ready to take any amount that can be supplied. The stamping capacity is 30,000 sec/day and a tea tray takes 20 sec to stamp, while an ash tray takes 10 sec to stamp. Forming capacity is the same as stamping but forming a tea tray takes only 5 sec while an ash tray takes 15 sec to be formed. Painting capacity is 40,000 sec/day requiring 10 sec for an ash tray and 8 sec for a tea tray. The net realization for a tea tray is Rs 2.50 with a variable cost of Rs 2.20. An ash tray fetches Rs 1.50 against a variable cost of Rs 1.30. The fixed expenses are Rs 350 per day.

(a) Formulate this product-mix problem as an LPP.

(b) How many ash and tea trays should be made everyday?

(

c) If sheet metal is controlled with an allocation of 3 60 square metres per day and a tea tray requires 0.2 square metres against 0.16 square metres for an ash traY, what will be the new product-mix?

(CA, November, 1976)