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A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z = 90p0.84 0.16 Chemical P costs $500 a unit and chemical R costs $4,500 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $843,750. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units

A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z = 90p0.84 0.16 Chemical P costs $500 a unit and chemical R costs $4,500 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $843,750. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units

Advanced Engineering Mathematics
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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**Problem Description:** A chemical manufacturing plant can produce \( z \) units of chemical Z given \( p \) units of chemical P and \( r \) units of chemical R, based on the equation: \[ z = 90p^{0.84}r^{0.16} \] - **Cost Information:** - Chemical P costs $500 per unit. - Chemical R costs $4,500 per unit. - **Budget Constraint:** - The company has a total budget of $843,750. **Questions:** - **A)** How many units of each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? - Units of chemical P, \( p = \) [Input box] - Units of chemical R, \( r = \) [Input box] - **B)** What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) - Max production, \( z = \) [Input box] units --- This setup requires solving for the optimal number of units of chemicals P and R that should be purchased to maximize the production of chemical Z. The solution will need to adhere to the budget constraint of $843,750 and take into account the cost per unit of each chemical. The equation provided for \( z \) reflects the production function dependent on the quantities of P and R.
Transcribed Image Text:**Problem Description:** A chemical manufacturing plant can produce \( z \) units of chemical Z given \( p \) units of chemical P and \( r \) units of chemical R, based on the equation: \[ z = 90p^{0.84}r^{0.16} \] - **Cost Information:** - Chemical P costs $500 per unit. - Chemical R costs $4,500 per unit. - **Budget Constraint:** - The company has a total budget of $843,750. **Questions:** - **A)** How many units of each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? - Units of chemical P, \( p = \) [Input box] - Units of chemical R, \( r = \) [Input box] - **B)** What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) - Max production, \( z = \) [Input box] units --- This setup requires solving for the optimal number of units of chemicals P and R that should be purchased to maximize the production of chemical Z. The solution will need to adhere to the budget constraint of $843,750 and take into account the cost per unit of each chemical. The equation provided for \( z \) reflects the production function dependent on the quantities of P and R.
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