Question

Jake’s is a burger restaurant that sells two main types of burgers. The company earns $6 on type 1
burger it sells and $10 on each type 2 burger. The burger paddies that Jake’s uses are actually preprepared
by another company. The supplier has a special order to fill for another customer and
cannot ship more than 80 type 1 and 75 type 2 burger paddies to Jake’s per day. The employees at
Jake’s must spend about 2 minutes preparing each type 1 burger they sell. They spend roughly 3
minutes to complete this process for type 2 burger. They expect to have about 301 minutes available
for this purpose during each day. The store’s management is fairly certain that they can sell all the
burgers for which they order paddies but are unsure how many type 1 and type 2 paddies they
should order to maximize profits.
a) (2 Points) Formulate an LP model for this problem.
b) (2 Points) Sketch the feasible region for this model.
c) (5 Points) Find the optimal solution using the simplex algorithm.

Answer 1

Since the profit is to be maximised, the objective function will be

Max 6X+10Y

where X is the number of type 1 burger made, while Y is type 2 burger made.

X<=80

Y<=75

2X+3Y<=301.

X=>0, Y=>0

The points of optimality are

(0.75) (80,0) ( 38.75) and ( 80,47)

Valu of OF on these points

(i) 10x75=750 0n (0.75)

(ii) 80x6=480 on (80,0)

(iii) 38x6+75x10=978

(iv) 80x6+47x10=950

The maximum value of profit 978 is obtained at x=38 y=75.