Question

Help me with the workings to these questions please!!!

Question 7 Not answered Marked out of 1.00 PFlag question The cost of producing x units of good 1 and y units of good2 is C-50r +cryIy 70.where c and h are constants. Marginal cost with respect to good 2 at x = 15, y = 34, c = 0.1 and h = 25 is (correct to 4 decimal places) Answer: The correct answer is: 25.0069 Question 8 Not answered Marked out of 1.00 P Flag question Answer For the function v = ar' + br' places) c , ifa-17, b = 17 and c-320, a local minimum occurs at which value of x (correct to four decimal The correct answer is:-0.7500

Answer 1

Ans7. Marginal cost = d(total cost) / d(quantity)

Marginal cost with respect to good 2:

= 1/4(c(x^1/2)y^(-3/4)) + h ......eq(1)

C = 0.1 ; h =25 , x =15 ; y = 34

Substituting the given values in eq(1)

1/4(0.1(15^(1/2) × 34^(-3/4)) + 25

= 25.0069

Ans 8.) To find the local minima , we first find the first derivative of the given equation with respect to 'x'

f'(y) = 4a(x^3) + 3b(x^2)

Put f'(y) = 0   

4a(x^3) + 3b(x^2)= 0

As , a = 17 , b = 17 , c = 320

x^2(4ax + 3b) = 0

Which gives ,

X^2 = 0 => x = 0

4ax + 3b = 0 => x = -3(17)/4(17)

=> x = -0.75

The 2 critical points are:

x = -0.75 ; x = 0

Put x = 0

f(0) = 17(0)^4 + 17(0)^3 + 320  

f(0) = 320

Put x = -0.75

f(-0.75) = 17(-0.75)^4 + 17(-0.75)^3 +320

f(-0.75) = 307.44

As we can see that the value of the given equation is low at x = -0.75.

So local minima = - 0.7500