A company produces two products. The revenue made by selling q₁ units of the first product and q2 units of the second product is given by r(9₁,92)=√√9₁² + 92² − 29192 +69₁ . The current production consists of 10 units of the first product and 12 units of the second product. a) Calculate (10,12) and - (10,12). Ər 292 b) The company will increase the production of the first product by 0.5 units and decrease the production of the second product by 1 unit. Do you expect the company to have a higher or a lower revenue? Use your answer to a)! Ər 0q1 c) We can approximate the given revenue function by a linear function f (91, 92) for values (91, 92) which are close to (10,12). Find the equation of this linear function and use this function to estimate the
A company produces two products. The revenue made by selling q₁ units of the first product and q2 units of the second product is given by r(9₁,92)=√√9₁² + 92² − 29192 +69₁ . The current production consists of 10 units of the first product and 12 units of the second product. a) Calculate (10,12) and - (10,12). Ər 292 b) The company will increase the production of the first product by 0.5 units and decrease the production of the second product by 1 unit. Do you expect the company to have a higher or a lower revenue? Use your answer to a)! Ər 0q1 c) We can approximate the given revenue function by a linear function f (91, 92) for values (91, 92) which are close to (10,12). Find the equation of this linear function and use this function to estimate the
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![A company produces two products. The revenue made by selling q₁ units of the first product and q2 units of
the second product is given by
2
= 91²
1² + 9₂² — 29192 +69₁.
r(9₁,92)
The current production consists of 10 units of the first product and 12 units of the second product.
a) Calculate (10,12) and -(10,12).
ər
292
b) The company will increase the production of the first product by 0.5 units and decrease the production
of the second product by 1 unit. Do you expect the company to have a higher or a lower revenue? Use
your answer to a)!
ər
0q1
c) We can approximate the given revenue function by a linear function f (9₁, 92) for values (9₁, 92) which
are close to (10,12). Find the equation of this linear function and use this function to estimate the
revenue made by producing 0.5 units more of the first product and 1 unit less of the second product.
Compare this result with the result you found in b).
d) The demand for both products is currently increasing at a rate of 1 unit per week. Use the chain rule
to determine approximately by what amount the revenue will change in half a week's time from now.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda1ab5de-bf4d-4028-8a6d-57425af6cfb9%2F01622ff6-a576-4d9d-8e9d-14c864ead4a7%2Fbx6pphq_processed.png&w=3840&q=75)
Transcribed Image Text:A company produces two products. The revenue made by selling q₁ units of the first product and q2 units of
the second product is given by
2
= 91²
1² + 9₂² — 29192 +69₁.
r(9₁,92)
The current production consists of 10 units of the first product and 12 units of the second product.
a) Calculate (10,12) and -(10,12).
ər
292
b) The company will increase the production of the first product by 0.5 units and decrease the production
of the second product by 1 unit. Do you expect the company to have a higher or a lower revenue? Use
your answer to a)!
ər
0q1
c) We can approximate the given revenue function by a linear function f (9₁, 92) for values (9₁, 92) which
are close to (10,12). Find the equation of this linear function and use this function to estimate the
revenue made by producing 0.5 units more of the first product and 1 unit less of the second product.
Compare this result with the result you found in b).
d) The demand for both products is currently increasing at a rate of 1 unit per week. Use the chain rule
to determine approximately by what amount the revenue will change in half a week's time from now.
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