1. A catering company needs to serve to 100 people for with the lowest budget B.
ID: 1132310 • Letter: 1
Question
1. A catering company needs to serve to 100 people for with the lowest budget B. They need to provide the food, F, as well as the cooking staff, S (can have partial units of F and S). Each unit of food costs PFf and each staff member costs Ps. The relationship between the inputs F and S and people served Q is Q-FS. The company needs to choose F and S to minimize B while still serving Q 100 people. a) What is the objective function for this problem? b) What is the constraint? c) Which of the variables, [B, F, S,Q, Pf, Ps}, are ex- ogenous? Which are endogenous? Explain. d) Write a complete statement of the constrained opti- mization problem anExplanation / Answer
Let price of food be Pf and price of staff Ps
a) B= Pf.F + Ps.S
Cost function is the objective function.
b) production function is a constraint.
Q= 100= FS
c) endogenous variables are the variables which we find from the model. Exogenous variables are already given.
d) minimise B= Pf.F + Ps.S subject to 100= FS
F and S are endogenous. B,Q,Pf and Ps are exogenously given.
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