Aretired 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 $6,950 and labor, materials, and transportation costs of $30 per car. the outside location would have fixed monthly costs of $4,350 and labor, materials, and transportation costs of $38 per car. dealer price at either location will be $98 per car.
a. which location will yield the greatest profit if monthly demand is (1) 330 cars? (2) 430 cars? 330 cars: yields the greatest profit. 430 cars: yields the greatest profit.
b. at what volume of output will the two sites yield the same monthly profit?

X = 325 cars will yield same profit in both locations

Explanation:

Location                                            City                                         Outskirts

Dealer Price                                        $                                            $

(98 x 330)                                       32340                                       32340

Labour,Material                                                                                    

and Transportation Cost              

($30/car x 330 cars)                         (9900)                                          

( $38/car x 330 cars)                                                                           (12540)

Fixed Cost                                          (6950)                                        (4350)

Profit                                                  15,490                                       15450

City will yield greatest profit if monthly demand is 330 cars

Location                                            City                                         Outskirts

Dealer Price                                        $                                            $

(98 x 430)                                           42,140                                     42,140                                      

Labour,Material                                                                                    

and Transportation Cost              

($30/car x 430 cars)                         (12900)                                          

( $38/car x 430 cars)                                                                           (16340)

Fixed Cost                                           (6950)                                        (4350)

Profit                                                   22,290                                       21450

City will yield greatest profit if monthly demand is 430 cars

b)

let X be the volume of output for both sites to yield same profit

City

Dealer Price = 98X

Labour, material and transportation= 30X

Fixed cost = 6950

Profit = 98X-(30X+6950)

Outskirts

Dealer Price = 98X

Labour,Material and transportation = 38X

Fixed Cost = 4350

Profit = 98X-(38X+4350)

Both Profits are same therefore

98X-30X-6950 = 98X-38X -4350

-30X+38X = -4350+6950

-8X = 2600

X = 325 cars will yield same profit in both locations

odd consecutive integers are odd integers that follow each other. they have a difference of 2 between every two numbers. if n is an odd integer, then n, n+2, n+4 and n+6 will be odd consecutive integers. the first number in the pattern is always the variable on its own or in this case, "n". examples.