Until recently, hamburgers at the city sports arena cost S2.50 each. The food co

Question

Until recently, hamburgers at the city sports arena cost S2.50 each. The food concessionaire sold an average of 875 hamburgers on game night. When the price was raised to $3.20, hamburger sales dropped off to an average of 700 per night The concessionaire's fixed costs were $1,027.20 per night and the variable cost was S0.76 per hamburger. Answer the following questions (A) through (D) (A) Assume that the relationship between price p and demand x is linear. Find the price-demand function, p(x) (B) Find the revenue function, R(x). Rx)- (C) Assume that the cost function is inear. Find the cost function, C(x). C(x)- (D) Find the profit function, P(x) P(x)-

Explanation / Answer

(x1,p1)=(875,2.5) ,(x2,p2)=(700,3.2)

(A)

p-2.5 =((3.2-2.5)/(700-875))(x-875)

=>p-2.5 =(0.7/(-175))(x-875)

=>p-2.5 =-0.004(x-875)

=>p-2.5 =-0.004x +3.5

=>p =6 -0.004x

so price-demand equation is p(x) =6 -0.004x

(B)

revenue,R(x) =xp

=>R(x) =x(6 -0.004x )

=>R(x) =6x -0.004x2

(C)

total cost =fixed cost +variable cost

C(x)=1027.2 +0.76x

(D)

profit = revenue -cost

=>P(x)=R(x)-C(x)

=>P(x)=6x -0.004x2-1027.2 -0.76x

=>P(x)= -0.004x2+5.24x -1027.2

PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

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