This is a question about microeconomics

l | You manage a clothing workshop that produces dresses by workers using machines. Let q be the total dresses that your workshop makes. L is the number of workers, and K is the number of machines. a) Suppose the production function of your workshop is given as: q = 4L\"'5 + 4K. Does the function exhibit increasing, constant or decreasing returns to scale? Show your analysis step by step. b) Suppose each worker costs w : $20 per hour, and each machine costs r : $40 per hour. Production costs are given by the cost of workers and machines, plus $10 per dress for raw materials, such as fabrics and threads. Assume the production is short-run and the capital input is fixed at I? = 5. 1What is the cost function of your workshop? How many workers are needed to produce 40 dresses? c) Based on your production func1ion, the marginal products can be derived as: MPL : 2L'"'5 and MPK : 4. Wi'l the input prices w : $20 and r : $4U,what is the optimal level of labor input? What is the corresponding l_eve1 of output? Calculate the total cost when the op1irnization occurs. (Realize: K = 5} d) Simplify your production function as: q = F(K, L), where K and L are capital and labor inputs with the prices of r and w. Assume the production function exhibits decreasing returns to scale. Determine if your production has economies or diseconomies of scale. Show your analysis clearly in steps. Demonstrate your nding in a diagram