Question

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 $100,000 to construct, requires 5 employees and has an expected revenue of $200,000. A full service restaurant costs $150,000 to construct, requires 15 employees, and has expected revenue of $500,000. The chain has $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. How many restaurants of each type should the chain open in order to maximize the expected revenue? How much of the capital will they use and how many employees will they hire?

Answer 1

To maximize the expected revenue, the fast food chain should determine the number of drive-through and full-service restaurants to open. Equations can be formed using the given constraints, and they can be solved to find the optimal values that maximize the expected revenue. The total capital used and the number of employees hired can then be calculated accordingly.

Step-by-step explanation:

To maximize the expected revenue, we need to determine the number of drive-through and full-service restaurants the fast food chain should open.

Let's assume the number of drive-through restaurants is 'x' and the number of full-service restaurants is 'y'.

From the given information, we can form the following equations:

Cost constraint: 100,000x + 150,000y <= 2,400,000

Labor constraint: 5x + 15y <= 210

Licensing constraint: x + y <= 20

Revenue constraint: 200,000x + 500,000y

We can solve these equations using a graphing calculator or algebraic methods to find the values of 'x' and 'y' that maximize the expected revenue.

Once the values of 'x' and 'y' are obtained, we can calculate the total amount of capital used by multiplying the cost of constructing each type of restaurant with their respective quantities (100,000x for drive-through and 150,000y for full-service).

In a similar way, we can calculate the total number of employees hired by multiplying the number of employees required for each type of restaurant with their respective quantities (5x for drive-through and 15y for full-service).