Respuesta :
Answer:
a. Average cost equation
[tex]\bar c=0.02Q+0.65+250Q^{-1}[/tex]
b. Q = 112 units
c. Average cost (Q = 112 units) = GHS 5.12
d. Usually, the actual production capacity.
Step-by-step explanation:
We will use $ as the currency symbol for GHS.
a) We have:
- Variable costs: 0.65Q
- Fixed costs: 250
- Special costs: 0.02Q^2
Then we can write the total cost equation as:
[tex]C(Q)=0.65Q+250+0.02Q^2[/tex]
The average cost function can be calculated dividing the total cost equation by Q. Then, we have:
[tex]\bar c=\dfrac{C(Q)}{Q}=\dfrac{0.02Q^2+0.65Q+250}{Q}=0.02Q+0.65+250Q^{-1}[/tex]
b) The output level that minimize the average cost can be calculated deriving the average cost equation and making it equal to zero:
[tex]\dfrac{d\bar c}{dQ}=0.02+(-1)250Q^{-2}=0.02-250Q^{-2}=0\\\\\\\dfrac{250}{Q^2}=0.02\\\\\\Q^2=250/0.02=12,500\\\\Q=\sqrt{12,500}\approx 112[/tex]
The output level that minimizes cost is Q=112 units.
c. The average cost of production for the output level of 112 is:
[tex]\bar c=0.02Q+0.65+250Q^{-1}\\\\\bar c(112)=0.02*112+0.65+250/112\\\\\bar c(112)=2.24+0.65+2.23\\\\\bar c(112)=5.12[/tex]
d. The limitation is not specified, by this models have a range of Q values where it is valid. These range is usually dependent on the scale of the production. The factory will have a maximum level of production, and over this level, the cost equation is different as other investments are needed.
