This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Step 1: Integrate the marginal cost function to find the cost function C(x). The marginal cost is given by (dC)/(dx) = 32 - 0.04x. To find C(x), we integrate (dC)/(dx) with respect to x: C(x) = (32 - 0.04x)\,dx C(x) = 32x - 0.04 (x^2)/(2) + K C(x) = 32x - 0.02x^2 + K where K is the constant of integration. Step 2: Use the given condition to find the value of K. It costs M50 to produce one shoe, which means C(1) = 50. Substitute x=1 and C(x)=50 into the cost function: 50 = 32(1) - 0.02(1)^2 + K 50 = 32 - 0.02 + K 50 = 31.98 + K K = 50 - 31.98 K = 18.02 Step 3: Write the complete cost function C(x). Substitute the value of K back into the cost function: C(x) = 32x - 0.02x^2 + 18.02 The cost function C(x) is: C(x) = -0.02x^2 + 32x + 18.02 Send me the next one 📸