The answer to part a is correct. I have tried several things for part b, but I c

Question

The answer to part a is correct. I have tried several things for part b, but I cannot get it. Please help

(1 point) A company manufactures zlunits of one item and y units of another. The total cost in dollars, Cl of producing these two items is approximated by the function (a) If the production quota for the total number of items (both types combined) is 176. find the minimum production cost. cost 100304 (b) Estimate the additional production cost or savings if the production quota is raised to 177 or lowered to 175 production cost or savings

Explanation / Answer

C(x,y)=4x2+3xy+7y2+600

a)x+y=176

=>y=176-x

C(x)=4x2+3x(176-x)+7(176-x)2+600

C(x)=8x2-1936x+217432

for minimum cost dC/dx=0, d2C/dx2>0

dC/dx=16x-1936+0 ,d2C/dx2=16>0

16x-1936=0

x=121

y=176-x

y=176-121

y=55

minimum production cost =C(121,55)

minimum production cost =100304

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b)C(x,y)=4x2+3xy+7y2+600

let g(x,y)=x+y-176

using lagrange multipliers

C=g

<8x+3y,3x+14y>=<1,1>

8x+3y= ,3x+14y=

8x+3y=3x+14y

5x-11y=0

we have x+y=176=>y=176-x

5x-11(176-x)=0

16x=11*176

x=121

y=176-x

y=176-121

y=55

8x+3y=

(8*121)+(3*55)=

=1133

when quota israised to 177 or lowered to 175 ,change in number of units produced=1

= change in cost/change in number of units produced

1133= change in cost/1

change in cost=1133

additional prodyction cost orsavings =1133 dollars

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