Question

Can you find the marginal profit of a,b and c?

Answer 1

keeping in mind that for a cost C(x) and profit P(x) and revenue R(x), the marginal cost, marginal profit and marginal revenue are respectively dC/dx, dP/dx and dR/dx, then


`\bf P(x)=0.03x^2-3x+3x^(0.8)-4400 \\\\\\ \stackrel{marginal~profit}{\cfrac{dP}{dx}}=0.06x-3+2.4x^(-0.2) \\\\\\ \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^(0.2)}\implies \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{(1)/(5)}} \\\\\\ \cfrac{dP}{dx}=0.06x-3+\cfrac{2.4}{\sqrt[5]{x}}`


`\bf a)\qquad \cfrac{dP}{dx}=0.06(200)-3+ \cfrac{2.4}{\sqrt[5]{200}} \\\\\\ b)\qquad \cfrac{dP}{dx}=0.06(2000)-3+\cfrac{2.4}{\sqrt[5]{2000}} \\\\\\ c)\qquad \cfrac{dP}{dx}=0.06(5000)-3+\cfrac{2.4}{\sqrt[5]{5000}} \\\\\\ d)\qquad \cfrac{dP}{dx}=0.06(10000)-3+\cfrac{2.4}{\sqrt[5]{10000}}`