Help on this would be really appreciated !

A powerplant produces electricity (E) from two inputs: Labor (L, week) and Coal (C, short tons). These are the only two inputs into production and there are no other costs involved. [Note: As always, assume that you can purchase non-integer amounts of C and L]. The Production Function of Electricity is: E = 100- Cos -L'2 Marginal products are as follows: MPC = 80 - {2-02 - l.\"2 and MP; =20- Ca"; 15"\" MP6_ 1. This means that the MRTSclL = MPL 4E. a) On a graph with Coal (C) on the horizontal axis and Labor (L) on the vertical axis, sketch the isoquants for E=20,000 and E=40,000. 1' Note: Simple sketches are sa'icient, no need for precise calculations] b) A short ton of Coal (C) initially costs $100 each, and each week of labor costs $1,000. What is the lowest-cost combination of C and L to generate electricity output E=20,000? What is the Average Cost (of both coal and labor) per unit of E? Add the cost-minimizing mix of inputs to your graph from (a), labelling it A. Also sketch the isocost line that passes through A, and label its' slope. c) Suppose the price of Coal (C) increases to $120. Calculate both the new cost-minimizing input mix and the cost of generating 13:20 ,000 of electricity. Add the cost-minimizing mix of inputs to your graph from (a), labeng it B. Also sketch the isocost line that passes through B. Are coal and labor complements or substitutes? d) Given your results from part (c), draw a new graph which shows the Input Demand of the powerplant for Coal (C), holding constant the production target E=20,000 and the price of Labor (L) at $1,000. Indicate the points corresponding to A and B on your new graph. [Hint: Place quantity of coal on the horizontal and price of coal on the vertical axis]