Asked by Anonymous
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.
Answers
Answered by
Anonymous
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
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
Answered by
oobleck
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