A retired auto mechanic hopes to open a rustproofing shop. Customers would be lo

Question

A retired auto mechanic hopes to open a rustproofing shop. Customers would be local new-car dealers. Two locations are being considered, one in the center of the city and one on the outskirts. The central city location would involve fixed monthly costs of $6,810 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,200 and labor, materials, and transportation costs of $40 per car. Dealer price at either location will be $90 per ca a. Which location will yield the greatest profit if monthly demand is (1) 200 cars? (2) 300 cars? yields the greatest profit. yields the greatest profit. 200 cars: Outside 300 cars: City b. At what volume of output will the two sites yield the same monthly profit? Volume of output cars

Explanation / Answer

For central city location

For outside location

Price(P) = $90 per car

a) If monthly demand(d) = 200 cars,

Total cost for city = FC + (dxVC) = $6810+(200x$30)= $6810+$6000 = $12810

Total cost for outside = FC+(dxVC) = $4200+(200x40)= $4200+$8000 = $12200

So for monthly demand of 200 cars, outside location should be chosed as it has a lower total cost than the city

If the monthly demand (d) = 300 cars,

Total cost for outside = FC+(dxVC) = $4200+(300x$40)= $4200+$12000 = $16200

Total cost for city = FC+(dxVC) = $6810+(300x$30)= $6810+$9000 = $$15810

So for the monthly demand of 300 cars the city lication should be chosen as it has a lower total cost than outside.

b) Let the volume of output = Q

Profit for outside location = profit for city location

=> Q(P-VC) - FC = Q(P-VC) - FC

=> Q(90-40)-4200 = Q(90-30)-6810

=> 50Q - 4200 = 60Q - 6810

=> 60Q - 50Q = 6810-4200

=> 10Q = 2610

=> Q = 2610/10

=> Q = 261 cars

So at the volume of output of 261 cars the two sites will yield the same monthly profit  

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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