3Given: Q = f(L.K) = KL2-L, where Q is outputand Land Kare the labor and capital inputs,respectively.Suppose K is a fixed input set at 15 units.Mathematically and graphically show theinput levels that divide stages i & II, andstages I| & III of production.

Consider the given equation, Q=KL2-L3 Since, we have given that K=15, so we get, Q=15L2-L3 The…

Answered: Given: Q = f(L.K) = KL2-L³, where Q is…

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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Let us consider the case of LaRosa Machine Shop (LMS). LMS is studying where to locate its tool bin facility on the shop floor. The locations of the five production stations appear in the figure below. Y 5 3 Min 2 Fabrication 1 Station Paint Paint Subassembly 1 Fabrication (x, y) = Subassembly 1 Subassembly 2 Assembly Subassembly 2 2 1 4 1 3 X Y Demand 3 2.5 2 4 2 Assembly 5 4 4 11 25 12 6 16 X = horizontal location of the tool bin Y = vertical location of the tool bin 5 In an attempt to be fair to the workers in each of the production stations, management has decided to try to find the position of the tool bin that would minimize the sum of the distances from the tool bin to the five production stations. We define the following decision variables. 6 e We may measure the straight line distance from a station to the tool bin located at (X, Y) by using Euclidean (straight-line) distance. For example, the distance from fabrication located at the coordinates (1, 4) to the tool bin located…
(b) Let xij be the amount shipped from source i to destination j in a 5X5 transportation problem, and let Cij be the corresponding transportation cost per unit. The amounts of supply at sources 1,2,3,4 and 5 are 210, 150,250,190 and 150 units respectively and the demands at destinations 1,2,3,4 and 5 are 205, 220,180,180 and 165 units respectively. The cost of shipping from source 1 to destinations 1,2,3,4 and 5 are 29, 28, 31, 27 and 32 respectively. The cost of shipping from source 2 to destinations 1,2,3,4 and 5 are 26, 27, 30, 37 and 31 respectively. The cost of shipping from source 3 to destinations 1,2,3,4 and 5 are 32, 38, 29, 27 and 35 respectively. The cost of shipping from source 4 to destinations 1,2,3,4 and 5 are 33, 39, 27, 29 and 33 respectively. The cost of shipping from source 5 to destinations 1,2,3,4 and 5 are 35,31, 34, 23 and 35 respectively. (i)Find the associated optimal cost. (ii)Determine each non basic variable.
In the production process of a company, 4 units of a certain input are used daily. It happens that the different formulations of this input can affect the yield of the process as well as the level of environmental pollution. On a given day the company has 40 units of this input in stock and they can be classified according to the table below:
Example 12.8. A firm uses milling machines, grinding machines and lathes to pro- duce two motor parts. The machining times required for each part, the machining times avail- able on different machines and the profit on each motor part are given below : Machining time reqd. for the motor part Max. time available per Type of machine (mts) week (minutes) I II 10 2,000 Milling machines Grinding machines Lathes. 2 900 12 3,000 Profit/ unit (Rs.) 100 40 Determine the number of parts I and II to be manufactured per week to maximize the profit. د ه
QUESTION 2 A tailor has the following materials available: 16 square yards of cotton, 11 square yards of silk, and 15 square yards of wool. A suit requires 2 square yards of cotton, 1 square yard of silk, and 1 square yard of wool. A gown requires 1 square yard of cotton, 2 square yards of silk, and 3 square yards of wool. Suppose the profit P is $30 on a suit and $50 on a gown. Find the maximum profit that can be made and the corresponding number of suits and gowns that yield the maximum profit. $ 310 Numbef of suits sold to gain max. profit. 7 Numbef of gowns sold to gain max. profit. 2
II) A firms production is represented by the following Cobb-Douglas function: Q = K13 L23. The rental rate, r, of capital is given by $16 and the price of labor is $4. a. For a given level of output, what should be the ratio of capital to labor in order to minimizecosts?b. How much capital and labor should be used to produce those 200 units?c. What is the minimum cost of producing 200 units?d. What is the additional cost of increasing output to 350 units in the short run and in the longrun?e. Does this production function exhibit increasing, decreasing, or constant returns to scale?Please answer based on the cost calculations in parts c and d.

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Given: Q = f(L.K) = KL2-L³, where Q is output and L and K are the labor and capital inputs, respectively. Suppose K is a fixed input set at 15 units. Mathematically and graphically show the input levels that divide stages I & II, and stages II & III of production.