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R TT Ov Management Kdan Cloud Share Tool Comment & Markup main-2-11 2 + A= Outlines Q Search ►Functions of two variables Solutions 136% T Annotation Editor FAX OCR Q OCR Convert Fax Search nations (qL, 9c) to generate 12 units a day are economically sound. 16. The production q (in units) of a certain good in terms of the amount q of labour invested and the amount qc of capital invested is given by the production function q = 5-qL2/3-qc1/3. At this moment, 512 units of labour and 1000 units of capital are invested daily. This means that at this moment, 3 200 units are produced daily. The graph below gives the contour line of level 3 200 of the production function. 1,500 1,400 gc 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 գլ Figure 8: Contour line of level 3 200 of the production function q. (a) Give an implicit and explicit equation of this contour line. Assume for this and later parts that a unit of labour costs 1.89 units of money and that a unit of capital costs 1.25 units of money. Moreover, there is a fixed cost of 14.3 units of money a day. (b) Give the equation of the cost function c(qL, 9c). (c) Graph, in Figure 8 above, a line that allows you to decide that there exists another combination (9L.qc) to generate 3 200 units a day with exactly the same cost as the combination (q1,qc) = (512, 1000). (d) Explain how you can approximately read this second combination from the graph above. (e) Calculate this second combination exactly. Make use of your graphing calculator. (f) Explain how you can graphically find the combinations to produce 3 200 units a day in a cheaper way than by investing (qL, 9c) = (512, 1000). (g) Describe the method to find the minimal budget to reach the daily production level q = 3200 geometrically. (h) Calculate the minimal cost to realize production level q = 3200 and the number of units of capital and labour that have to be invested. 9 /10

R TT Ov Management Kdan Cloud Share Tool Comment & Markup main-2-11 2 + A= Outlines Q Search ►Functions of two variables Solutions 136% T Annotation Editor FAX OCR Q OCR Convert Fax Search nations (qL, 9c) to generate 12 units a day are economically sound. 16. The production q (in units) of a certain good in terms of the amount q of labour invested and the amount qc of capital invested is given by the production function q = 5-qL2/3-qc1/3. At this moment, 512 units of labour and 1000 units of capital are invested daily. This means that at this moment, 3 200 units are produced daily. The graph below gives the contour line of level 3 200 of the production function. 1,500 1,400 gc 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 գլ Figure 8: Contour line of level 3 200 of the production function q. (a) Give an implicit and explicit equation of this contour line. Assume for this and later parts that a unit of labour costs 1.89 units of money and that a unit of capital costs 1.25 units of money. Moreover, there is a fixed cost of 14.3 units of money a day. (b) Give the equation of the cost function c(qL, 9c). (c) Graph, in Figure 8 above, a line that allows you to decide that there exists another combination (9L.qc) to generate 3 200 units a day with exactly the same cost as the combination (q1,qc) = (512, 1000). (d) Explain how you can approximately read this second combination from the graph above. (e) Calculate this second combination exactly. Make use of your graphing calculator. (f) Explain how you can graphically find the combinations to produce 3 200 units a day in a cheaper way than by investing (qL, 9c) = (512, 1000). (g) Describe the method to find the minimal budget to reach the daily production level q = 3200 geometrically. (h) Calculate the minimal cost to realize production level q = 3200 and the number of units of capital and labour that have to be invested. 9 /10

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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R TT Ov Management Kdan Cloud Share Tool Comment & Markup main-2-11 2 + A= Outlines Q Search ►Functions of two variables Solutions 136% T Annotation Editor FAX OCR Q OCR Convert Fax Search nations (qL, 9c) to generate 12 units a day are economically sound. 16. The production q (in units) of a certain good in terms of the amount q of labour invested and the amount qc of capital invested is given by the production function q = 5-qL2/3-qc1/3. At this moment, 512 units of labour and 1000 units of capital are invested daily. This means that at this moment, 3 200 units are produced daily. The graph below gives the contour line of level 3 200 of the production function. 1,500 1,400 gc 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 գլ Figure 8: Contour line of level 3 200 of the production function q. (a) Give an implicit and explicit equation of this contour line. Assume for this and later parts that a unit of labour costs 1.89 units of money and that a unit of capital costs 1.25 units of money. Moreover, there is a fixed cost of 14.3 units of money a day. (b) Give the equation of the cost function c(qL, 9c). (c) Graph, in Figure 8 above, a line that allows you to decide that there exists another combination (9L.qc) to generate 3 200 units a day with exactly the same cost as the combination (q1,qc) = (512, 1000). (d) Explain how you can approximately read this second combination from the graph above. (e) Calculate this second combination exactly. Make use of your graphing calculator. (f) Explain how you can graphically find the combinations to produce 3 200 units a day in a cheaper way than by investing (qL, 9c) = (512, 1000). (g) Describe the method to find the minimal budget to reach the daily production level q = 3200 geometrically. (h) Calculate the minimal cost to realize production level q = 3200 and the number of units of capital and labour that have to be invested. 9 /10
Transcribed Image Text:R TT Ov Management Kdan Cloud Share Tool Comment & Markup main-2-11 2 + A= Outlines Q Search ►Functions of two variables Solutions 136% T Annotation Editor FAX OCR Q OCR Convert Fax Search nations (qL, 9c) to generate 12 units a day are economically sound. 16. The production q (in units) of a certain good in terms of the amount q of labour invested and the amount qc of capital invested is given by the production function q = 5-qL2/3-qc1/3. At this moment, 512 units of labour and 1000 units of capital are invested daily. This means that at this moment, 3 200 units are produced daily. The graph below gives the contour line of level 3 200 of the production function. 1,500 1,400 gc 1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 գլ Figure 8: Contour line of level 3 200 of the production function q. (a) Give an implicit and explicit equation of this contour line. Assume for this and later parts that a unit of labour costs 1.89 units of money and that a unit of capital costs 1.25 units of money. Moreover, there is a fixed cost of 14.3 units of money a day. (b) Give the equation of the cost function c(qL, 9c). (c) Graph, in Figure 8 above, a line that allows you to decide that there exists another combination (9L.qc) to generate 3 200 units a day with exactly the same cost as the combination (q1,qc) = (512, 1000). (d) Explain how you can approximately read this second combination from the graph above. (e) Calculate this second combination exactly. Make use of your graphing calculator. (f) Explain how you can graphically find the combinations to produce 3 200 units a day in a cheaper way than by investing (qL, 9c) = (512, 1000). (g) Describe the method to find the minimal budget to reach the daily production level q = 3200 geometrically. (h) Calculate the minimal cost to realize production level q = 3200 and the number of units of capital and labour that have to be invested. 9 /10
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