A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r unitsof chemical R, where:z = 160p",0.4Chemical P costs Ş400 a unit and chemical R costs $2,800 a unit. The company wants to produce as manyunits of chemical Z as possible with a total budget of $420,000.A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Zsubject 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 youranswer to the nearest whole unit.)Max production, z=units

Given,z=160 p0.6r0.4P=$400, R=$2,800400P+ 2800R=420,000 To find: A) Units of chemical P,(p) and…

Answered: A chemical manufacturing plant can…

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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A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: Chemical P costs $100 a unit and chemical R costs $400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $80,000. 2= 100p0.8.0.2 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 manufacturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? 24 (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting…
(c) A storekeeper has 60m available for storage of two brands of mineral, drink X and Y. The volume of a crate of X is 3m' and that of a crate of Y is 2m'. A crate of X costs GH¢15, a crate of Y costs GH¢30, and he makes a profit of GH¢5 per crate of either brand. He has GH¢450 to spend on the order of purchases of x crates of X and y crates of Y. (i) Write down all the inequalities involving xr and y. (ii) Illustrate graphically the set P satisfying the inequalities. (iii) Find the maximum profit. (1 + i)' - 1 =2a + (n-1)d], T, = a+ (n-1)d, VANU,I %3D
A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in capital, K, resulting from an…
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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 = 100p-75,0.25 Chemical P costs $100 a unit and chemical R costs $700 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $112,000. 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

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