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

≤

Step-by-step 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