Math Problem Statement

SOLVER

En una empresa se sabe que al producir q unidades de determinado artículo el costo total está dado por: C(q) = (1/4)q^2 + 4q + 120 soles. El precio por unidad, en soles, depende del número de unidades producidas y está dado por p = 31 - 0.05q. Determine la utilidad máxima. ¿A qué precio se maximiza la utilidad?

Solution

I will first analyze the image to extract its mathematical content and then provide a solution. Please give me a moment. PIL import Image

Load the uploaded image to inspect it

img_path = "/mnt/data/1733695634872texlx16r.jpg" img = Image.open(img_path) img.show()It seems that the image has been displayed for inspection. Let me now extract the mathematical content from the image and analyze it to solve the problem.I am unable to directly extract the mathematical content from the image. However, if you can provide a description of the problem or manually input the key details, I will be able to assist you further. Would you like to do that?

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Math Problem Analysis

Mathematical Concepts

Optimization
Quadratic Functions
Profit Maximization

Formulas

C(q) = (1/4)q^2 + 4q + 120
p(q) = 31 - 0.05q
Revenue R(q) = p(q) * q
Profit U(q) = Revenue - Cost

Theorems

Critical Point Theorem
Second Derivative Test

Suitable Grade Level

Undergraduate - Economics/Mathematics

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