This is all the info there is. I don't understand how to derive the Euler equation when the adjust cost function doesn't have K in it

Consider the infinite horizon model of a firm facing adjustment costs to invest- ment. The firm pays a corporate income tax, Tt, and it also benefits from an investment tax credit, at the rate se on its investment expenditures. For the sake of simplicity, we assume that the tax credit applies to total investment cost, including adjustment cost. The firm managers maximizes its present value of the firm, V 1 VO +nje {(1 7o)F(K.) Pki(1 8:1)[e+C(1)}} (1) t=0 where F(Kt), is the net output from using the capital stock Kt, (F' > 0 and F" 0) 1. Denoting by at the shadow value of the capital stock (a) Write the firm optimization problem using the Lagrangian approach (make sure to indicate all decision variables) (3 points) (b) Derive and interpret all the first-order conditions of this problem. (10 points) (c) Using the investment Euler equation, and making the appropriate assumptions, determine the expression of the shadow value of capital, 9t. Interpret this expression. (7 points) 2. Determine the expression of the firm's investment demand function. In- terpret. (5 points) Consider the infinite horizon model of a firm facing adjustment costs to invest- ment. The firm pays a corporate income tax, Tt, and it also benefits from an investment tax credit, at the rate se on its investment expenditures. For the sake of simplicity, we assume that the tax credit applies to total investment cost, including adjustment cost. The firm managers maximizes its present value of the firm, V 1 VO +nje {(1 7o)F(K.) Pki(1 8:1)[e+C(1)}} (1) t=0 where F(Kt), is the net output from using the capital stock Kt, (F' > 0 and F" 0) 1. Denoting by at the shadow value of the capital stock (a) Write the firm optimization problem using the Lagrangian approach (make sure to indicate all decision variables) (3 points) (b) Derive and interpret all the first-order conditions of this problem. (10 points) (c) Using the investment Euler equation, and making the appropriate assumptions, determine the expression of the shadow value of capital, 9t. Interpret this expression. (7 points) 2. Determine the expression of the firm's investment demand function. In- terpret. (5 points)