Answer:
A. 120
B. 126
C. x=12
D. x=5
Step-by-step explanation:
A. Calculation to determine the Marginal Product (MP) when X = 8
Production function=Q=72x+15x^2-x^3
Let x be 8
Marginal Product (MP)=dQ/dx
Marginal Product (MP)=72x+15x^2-x^3
Marginal Product (MP)=72+30x-3x^2
Now let plug in X = 8
Marginal Product (MP)=72+30(8)-3(8)^2
Marginal Product (MP)=72+240-192
Marginal Product (MP)=120
Therefore the Marginal Product (MP) when X = 8 will be 120
B. Calculation to determine the Average Product (AP) when X = 6
Average Product (AP)=Q/X
Average Product (AP)=72+15x-x^2
Let plug in x=6
Average Product (AP)=72+15(6)-(6)^2
Average Product (AP)=72+90-36
Average Product (AP)=126
Therefore the Average Product (AP) when X = 6 is 126
C. Calculation to determine at what value of X will Q be at its maximum
Maximizing Q=dQ/dx=0
Maximizing Q=72+30x-3x^2=0
Maximizing Q=3x^2-30x-72=0
Maximizing Q=x^2-10x-24=0
Maximizing Q=x^2-12x+2x-24=0
Maximizing Q=x(x-12)+2(x-12)=0
Hence:
x=12 or (x=-2)
Therefore at what value of X will Q be at its maximum will be at x=12
D. Calculation to determine At what value of X will Diminishing Returns set in
Diminishing returns=dMP/dx=d²Q/dx²
Diminishing returns=30-6x<0
Hence:
x=30/6<0
x=5<0
Therefore at what value of X will Diminishing Returns set in will be at x= 5 or when MP is at a MAXIMUM VALUE.