I don't know how to answer (a), (b), (c) ...

Exercise 3 (15 points) Part d, e, f, g, h and i of this exercise should be solved using Excel, R, Matlab or Octave. Describe precisely all your steps and attach the results (numerical results and plots) to the assignment. Imagine you are a production manager in the company EVERYDAY. Currently, you are planning the production for the first quarter of 2020. The firm pursues a just-in-time production strategy. This means that you sell all the products the same day you produce them. You sell the products at a price P. You have price data for the first quarter of 2019. You expect that price will move the same way in 2020 as it did in 2019 (price data for 2019 can be found in the excel file available on Moodle). Your production function is given by F(K,L) = AKY?[1/? where A is a technology, K is a capacity and L is a labour. The daily cost of maintaining capacity K is D(K) = K3. There are no further costs for capacity (e.g. rent costs). The capacity level cannot be changed within the quarter. The capacity costs have to be paid irrespective of whether you produce or not. Furthermore, each day you hire labour L R, L 0. You pay a salary of w. (a) Write down the optimization problem in standard form. Is constraint qualification satisfied? What does this imply? (b) Write down the KT conditions. (c) Is the problem guaranteed to have a solution? Is the solution to the problem unique? Why (not)