Question

6-19 A chemical processing unit has a capacity for producing I million kg of a product per year. After the unit has been put into operation, it is found that only 500,000 kg of the product can be sold per year. An analysis of the existing situation shows that all fixed and other invariant charges, which must be paid whether or not the unit is operating, amount to 35 percent of the total product cost when operating at full capacity. Raw material costs and other production costs that are directly proportional to the quantity of production (i.e., constant per kilogram of product at any production rate) amount to 40 percent of the total product cost at full capacity. The remaining 25 percent of the total product cost is for variable overhead and miscellaneous expenses, and the analysis indicates that these costs are directly proportional to the production rate during operation raised to the 1.5 power. What will be the percent change in total cost per kilogram of product if the unit is switched from the original design rate of I 06kg/yr of product to a time and rate schedule which will produce 0.5x 106 kg or "half that amount" of product per year at the least total cost?

Answer 1

Actual production capacity is 1 million I.e 10,00,000 original rate is 106 /- so total cost is 106*10,00,000=1,06,00,00,000. But it sells only 5,00,000 kgs with 106/- so total cost is 5,00,000*0.5*106=265,00,000 so total cost change is 25 %..