Jamie will choose between two catering companies for an upcoming party. Company A charges a set up fee of $ 500 plus $25 for each guest. Company B charges a set up fee of $200 plus $ 30 per guest
a) Write expression that you can use to determine the amount each company charges for g guests .
b) Jamie learns that the $ 500 set up fee for company A includes payment for 20 guests. The $25 per guests charge is for every guest over the first 20.If there will be 50 guests , which company will cost the least ? Explain.

The correct answer is: From Equations vi & vii, we can conclude that Company A will cost the least.

Step-by-step solution:-
a). As per the given information, we get-
Setup fees for Company A = $ 500
Variable charges for Company A = $ 25 per guest
Setup fees for Company B = $ 200
Variable charges for Company B = $ 30 per guest
Now, we know that-
For Company A-
Variable charges = Number of guests × price per guest
∴ Variable charges = g × 25 ................................................................................................... (From given information)
∴ Variable charges = 25g ....................................................................................................... (Equation i)
Amount charged for g guests = Setup charges + Variable charges
∴ Amount charged for g guests = 500 + 25g ......................... (From given information & Equation i) ............. (Equation ii)
For Company B-
Variable charges = Number of guests × price per guest
∴ Variable charges = g × 30 ................................................................................................... (From given information)
∴ Variable charges = 30g ....................................................................................................... (Equation iii)
Amount charged for g guests = Setup charges + Variable charges
∴ Amount charged for g guests = 200 + 30g ......................... (From given information & Equation iii) ............. (Equation iv)
b). As per the second situation,
Total number of guests = g = 50
Also,
Variable cost for company A = price per guest × (Number of guests - 20) ….................. (because setup fees includes charges for 20 guests)
∴ Variable cost for company A = 25 × (50 - 20)
∴ Variable cost for company A = 25 × 30
∴ Variable cost for company A = $ 750 ......................................................................... (Equation v)
All the other information remains the same.
∴ Amount charged by Company A = Setup charges + Variable charges
∴ Amount charged by Company A = 500 + 750 ............................................................... (From given information & Equation v)
∴ Amount charged by Company A = 1,250 ...................................................................... (Equation vi)
Also,
Amount charged by Company B = 200 + 30g ............................................................... (From Equation iv)
∴ Amount charged by Company B = 200 + (30 × 50) ....................................................... (Total guests = 50)
∴ Amount charged by Company B = 200 + 1,500
∴ Amount charged by Company B = 1,700 ..................................................................... (Equation vii)
Final Answer:-
∴ From Equations vi & vii, we can conclude that Company A will cost the least.

In this question, the answer is to find out with the help of the fixed cost and variable cost formulas. So let's first understand what variable and fixed costs mean and the formula to calculate costs.
Variable costs are expenses that varies in proportion to the number of goods or services produced by a company. In other words, they are costs that vary with the amount of activity. As a result, the costs rise as the volume of activities rises and fall as the volume of activities falls.
Total Variable Cost = Total Output Quantity x Variable Cost Per Unit Output.
A fixed cost is any business expense that does not change in response to production or sales. Fixed costs are also known as indirect costs or overhead. Fixed costs cannot be changed to reduce expenses. Instead, they typically rely on an outside entity, such as a landlord or bank. Fixed costs include rent, insurance, and labor costs.
Fixed cost = Total cost of production - (No. of units produced x Variable cost per unit)
To find the total cost,
Total cost= Fixed cost + Variable cost