Homework 091012

Problem 1:

Total Cost: 300 +  75q + 5q^2
Price: 825 - 20q

#1.  Profit = (825 -20q) q - 300 - 75q - 10q
       P = 825Q - 20Q^2 - 75 - 10Q
       P = 825 - 40Q - 75 - 10Q     
       P  = 750 - 30q

#2. Thus,

      dTR = 750/30q  = 25q**
       dQ

#3. Price:   825 - 20(25) = 325

      Min: 25; Max: 30

#4. TR= (825 - 20(25)) (25)
      = 325 * 25
      = 8 ,125

#5. TC=  75Q + 5Q^2
           =  75(25) + 10(25)
           = 2,125

#6. Profit =6000


Problem 2:
TC = 34 + 80Q + 12Q^2
 P = 160 + 2Q

Profit =160q + 2q^2 - 34 - 80q- 24q
      P= 160q + 4q - 80q -24q
      P = 80 - 20q (1st "D")

Thus,

dTR= 80-20q = 4
dQ

Price=  P = 160 + 2(4) = 168

Min: 4; Max: 20


TR= (160 + 2(4)) (4) = 672

TC =  80(4) +24(4) = 416

Profit = 256