Possibility Restaurant

Angela and Zooey decided to open a french restaurant.

Initially they decided to serve only 2 full course meals , one with beef and other with fish.

The problem for them was to identify how many meals to prepare each night.

They estimated a max. sale of 60 meals per night.

Fish meal requires 15 min to prepare .

Beef meal requires 30 min to prepare.

Total kitchen staff labor available was 20 hrs for each day.

Angela and Zooey believed that they could sell at least 3 fish dinners for every 2 beef dinners.

They also believed that at least 10% of the customers will order beef dinner.

Profit for each fish dinner = $12.

Profit for each beef dinner = $16.

Clearly define the decision variables.

Construct the objective function.

Formulate the constraints.

Finding the optimal solution.

DECISION VARIABLES:

X1= Number of fish meals to be prepared each night.

X2= Number of beef meals to be prepared each night.

OBJECTIVE FUNCTION:

MAX Z = $12x1 + $16x2.

CONSTRAINTS :

x1 + x2 ≤ 60 (No. of meal constraint)

x1/4 + x2/2 ≤ 20 (Time Constraint)

x1/x2 ≥ 3/2 (Health Constraint)

x2 ≥ 0.1 (x1 + x2 )(Percent Constraint)

Non negativity constraints :

x1 , x2 ≥ 0

FOR POINT A : ( 240/7 , 160/7 )

Z : $777.4

FOR POINT B : ( 40 , 20 )

OPTIMAL SOLUTION

Z : $800

FOR POINT C : ( 54 , 6 )

Z : $744

The maximum profit is at point B which is $800. so the optimal solution is ,