Suppose the production function for firm Beta can be represented as q=f(K, L)=0.5*(L+2K), where L is the amount of labor used and K the amount of capital used. a) What kind of production function does the firm have? b) Draw two isoquant curves and label two points on each curve (put labor L on horizontal axis). c) Does this production function exhibit increasing return to scale, decreasing return to scale or constant return to scale? Prove your answer mathematically (Hint: you need to show your work by comparing i.e. f(2K, 2L) and 2f(K, L)). d) If w=$10 and r=$25, calculate the K and L that will produce q=300 in the least costly way. Hint: in this scenario, firm will only use the relatively cheaper input for production. e) Calculate the average cost when the firm is producing q=300 in the least costly way.