My Notes Ask Your T 4. 1.114 points I Previous Answers HarlMathAp11 12 4.007 Cos

Question

My Notes Ask Your T 4. 1.114 points I Previous Answers HarlMathAp11 12 4.007 Cost, revenue, and profit are in dollars and x is the number of units. firm knows that its marginal cost for a product is MC-3X+25, that its marginal revenue is MR-57-5x, and that the cost of production of 80 units is $11,800 (a) Find the optimal level of production. units (b) Find the profit function. (c) Find the profit or loss at the optimal level. There is a Select-of s Need Help? Read it Your work in queston(s) 5 will also be submitted or saved. Submit Assignment Save Assignment Progress Practice Another Version |

Explanation / Answer

total cost,C(x) = MC dx

C(x)=(3x+25) dx

C(x)=(3/2)x2 +25x +k

C(80)=11800

=>(3/2)*802 +25*80 +k =11800

=>k=200

total cost ,C(x)=(3/2)x2 +25x +200

when no units are sold there wont be any revenue

so

total revenue,R(x)= MR dx

R(x)=(57-5x) dx

R(x)=57x- (5/2)x2

(a)

at optimal level of production ,MR =MC

=>57-5x=3x+25

=>8x=32

=>x=4

optimum level is 4 units

(b)

profit ,P(x) =R(x)-C(x)

=>P(x) =[57x- (5/2)x2]-[(3/2)x2 +25x +200]

=>P(x) =-4x2 +32x -200

(c)

at optimum level

P(4) =-4*42 +32*4 -200

=>P(4) =-136

P(4)<0

there is a loss of $ 136

please rate if helpful. please comment if you have any doubt

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.