The Cobb-Douglas production function for a particular product is N(x, y)=40 x^0.8 y^0.2, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $80 and each unit of capital costs $120.

If $1, 200,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production.

Production will be maximized when using units of labor and ___units of capital.

the answer is 489

step-by-step explanation:

salary

step-by-step explanation:

x=6 and x=3

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< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)