United Auto Industries (Pvt) Ltd was established in 1999 under the leadership of Mr. Sana Ullah Chaudhary. This company has introduced economical 4- stroke motorcycles and Rickshaws by the name of UNITED. Day by day the market share of united motorcycles is increasing. Currently production capacity is 450000 units per annum in 8 hours shift. United Auto Industries (Pvt) Ltd is partner of many organizations at Federal and provincial level with Government. This company observed all standards of quality set by Pakistan Standard and Quality Control Authority (PSQCA). It has professionals in all the departments like Marketing & Sales, Quality Control, Production and Finance & Accounts.

Suppose the production function of the United Auto Industries (Pvt) Ltd according to degree of power is Q = 10 + 27L + 6L²- 12L³where Q and L refer, respectively, to the quantities of output and labor.

Requirements:

1. Being a student of economics identify the type of production function given in above case and also interpret the given production function.
2. Suppose United Auto Industries (Pvt) Ltd. uses labor, capital, and energy inputs in fixed proportion for the production of 4-stroke motorcycles. Does this means return to scale will be constant? Give your answer with logic.