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The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q) = 110g R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(g)= Evaluate P"(q) at your critical point. The result is negative which means that the profit is concave down at the critical point, and the critical point is a maximum.

The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q) = 110g R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(g)= Evaluate P"(q) at your critical point. The result is negative which means that the profit is concave down at the critical point, and the critical point is a maximum.

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
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Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...
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The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q) = 110g R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(g)= Evaluate P"(q) at your critical point. The result is negative which means that the profit is concave down at the critical point, and the critical point is a maximum.
Transcribed Image Text:The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q) = 110g R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(g)= Evaluate P"(q) at your critical point. The result is negative which means that the profit is concave down at the critical point, and the critical point is a maximum.
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