P(x) = R(x) - C(x) = -1000 + 500 x - 0.6 x^2
dP/dx = 500 - 1.2 x
d^2P/dx^2 is -1.2 for all x so max when dP/dx = 0
max profit when x = 500/1.2 = 417
if x = 15
R = 800*15 - 0.6*225 = 12000-135 = 11,865
C = 1000 + 300 (15) = 1000 + 4500 = 5,500
P = R-C = 6,365
dP/dx = 500 - 1.2*15 = 482
dR/dx = 800 - .6*225 = 800 - 135 = 665
dC/dx = 300 always
etc, you can do for 42
Suppose the total cost in dollars per week by Capital Corporation for producing its best-selling product is given by 𝐶(𝑥) = 1000 + 300𝑥. The revenue function for the production of the product was derived to be 𝑅(𝑥) = 800𝑥 − 0.6𝑥2. Analyse the profit function for the manufacturing of 𝑥 products, as well as interpret what the marginal cost and marginal revenue of 15 products signifies. Additionally, determine the exact and approximate profit from the manufacturing of the 42nd product.
2 answers
marginal cost/revenue = dC/dx or dR/dx
profit p(x) = R(x)-C(x) = -0.6x^2 + 500x - 1000
the marginal profit is thus dp/dx = -1.2x+500
for the 42nd unit, that would be 449.6
the exact profit would be p(42)-p(41) = 450.2
profit p(x) = R(x)-C(x) = -0.6x^2 + 500x - 1000
the marginal profit is thus dp/dx = -1.2x+500
for the 42nd unit, that would be 449.6
the exact profit would be p(42)-p(41) = 450.2
2 answers