Question

The firm's fixed cost is given as #1000 and over head coat of #12 per CD produced. Given the demand function for the firm
P=30-0.2√q
Where q is quantity produces and p is price. If the firm aims profit (π) of #20000 per month. Howany quantity (q) should be produced to realize this firm?

Answer 1

Profit to be achieved set by the firm at # 20,000, fixed costs at # 1000 and additional overhead cost per cd produced at # 12

Firm demand function $p = 30-0.2\sqrt{q}$

$Profit(Pq)=20000=R(q)–C(q)$

Where R (q) is the revenue and C (q) is the total cost P is the price and q is the quantity

$R(q)=q(30−0.2\sqrt{q}=30q–0.2q^\frac{3}{2}$

$C(q)=1000+12q$

Profit equation = $30q–0.2q^\frac{3}{2}$ $−(1000+12q)$

$0=18q−$$0.2q^\frac{3}{2}$ $−1000$

Maximum profit can be only found when the first derivative $\int$ q= 0

$\int\limits_{x\in C}dx$ q=$(90q−q^\frac{3}{2}−5000)$ $\int\limits_{x\in C}dx$

$0= 90- \frac{3}{2} q^\frac{1}{2}$

$q^\frac{1}{2}$ =90$\times \frac{2}{3}$

$q=60^{2}=$ 3600

quantity= 3600

This is the maximum quantity that can be produced to realize maximum profit that will be higher that # 20000