A3. A company produces and sells on two products x and y for which the demand functions are x = A= P₂, y = B -0.5Py, with P and Py being their prices and A > 0, B > 0. The combined production cost is C = x² + xy + y² + 10. Find the profit maximising level of output for each product x, y; the profit maximising price of each product; and derive conditions needed for x ≥ 0, y ≥ 0. Show also by considering the Hessian matrix that the profit is indeed maximised. Considering A = 30, B = 25, calculate the above quantities as well as the maximum profit/loss.
A3. A company produces and sells on two products x and y for which the demand functions are x = A= P₂, y = B -0.5Py, with P and Py being their prices and A > 0, B > 0. The combined production cost is C = x² + xy + y² + 10. Find the profit maximising level of output for each product x, y; the profit maximising price of each product; and derive conditions needed for x ≥ 0, y ≥ 0. Show also by considering the Hessian matrix that the profit is indeed maximised. Considering A = 30, B = 25, calculate the above quantities as well as the maximum profit/loss.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A3. A company produces and sells on two products x and y for which the demand functions are
x = A= P₂, y = B -0.5Py,
with P and Py being their prices and A > 0, B > 0. The combined production cost is C =
x² + xy + y² + 10. Find
the profit maximising level of output for each product x,y;
the profit maximising price of each product; and derive conditions needed for x ≥ 0, y ≥ 0.
Show also by considering the Hessian matrix that the profit is indeed maximised. Considering
A = 30, B = 25, calculate the above quantities as well as the maximum profit/loss.
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