Solve Exercise E7 taking simultaneously into account the data from Exercises E8 and E9.

Exercise E7

There are given:

Exercise E8

Solve Exercise E7, when the production total cost function has a form:

Exercise E9

Solve Exercise E7 assuming additionally that resources of production factors 

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X = (X1, x) (0, 0)-a vector of inputs of production factors, y = f(x)-an output level described by an increasing, strictly concave and twice differentiable production function, (#) > 0a price of a product manufactured by a monopoly as a function of product supply, set by a monopoly, p(f (x)) = () > 0-a price of a product manufactured by a monopoly as a function of production factors' inputs, c(x) = (C(x1), C2(x2)) (0, 0)-a vector of prices of production factors, each of whom is a function of demand reported by a monopoly for a given production factor, ci (x) = axi-a price of i-th production factor is proportional to the demand for i-th factor, r(y) = p(y)y-revenue (turnover) from sales of a manufactured product as a function of product supply, r(x) = p(f(x)) f(x)-revenue (turnover) from sales of a manufactured product as a function of inputs of production factors, clot (x) = C (x)x1 + C(x2)x2 + d = a(x +x2)+d-total cost of production, c(x) = C (x)x + c (x)x = a (x + x2)-variable cost of production, cf (x)= d-fixed cost of production, c(y) minimum cost of producing y output units, derived as an objective function corresponding to an optimal solution to problem (P2m), (y) =r(y) - c(y) = p(y)y c(y)-firm's profit as a function of output level, (x) = (x) - clot (x)-firm's profit as a function of inputs of production factors. For a production function: