Question

7. A fast-food chain plans to expand by opening several new restaurants. The chain operates two types of
restaurants, drive-through and full-service. A drive-through restaurant costs RM 100.000 to construct,
requires 5 employees, and has an expected annual revenue of RM 200.000. A full service restaurant
costs RM 150.000 to construct, requires 15 employees, and has an expected annual revenue of RM
500,000. The chain has RM 2,400,000 in capital available for expansion. Labor contracts require that
they hire no more than 210 employees, and licensing restrictions require that they open no more than
20 new restaurants.
(a) How many restaurants of each type should the chain open in order to maximize the expected
revenue? [1 point)
​

Answer 1

≤

Explanation:

                               Drive through                Full Service

Annual revenue          200,000                       500,000

Cost                               100,000                        150,000

Income                           100,000                        350,000

Employee                            5                                   15

Income / employee         20,000                        23,333.33

Using simultaneous equation ,

Let X represent the drive through service  ,and Y represent the full service restaurant

Budget = 100,000x + 150,000y ≤ 2,400,000  (equation 1)

Employer = 5x + 15y ≤ 210   (equation 2)

(Divide equation 1 by 10 ,000)

                     10x+ 15y ≤ 240 (equation 3)

Using elimination method, multiply equation 2 by -2

                      10x +15y ≤240

                      -10x - 30y ≤-420

                        -15y ≤ -180

                             y≤ -180/-15

y = 12

substitute y = 12 in equation 3

10x + 15y≤240

10x +180 ≤240

10x≤240-180

10x≤60

x≤6

                   

12         1,800,000      180

6           600,000         30

6 drive through services and 12 full services should be opened.

                           6 Drive through                12 full service            20

Cost                             600,000                      1,800,000           2,400,000

Employees                      30                                 180

Net income                     600,000                    4,200,000