Question

Linear Program Formulation Problem

Gillian’s restaurant has an ice cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week and the store has enough freezer space for 115 gallons in total. A gallon of ice cream costs $0.93 and a gallon of frozen yogurt costs $0.75 and the restaurant budgets $90 per week for purchasing these two items. The manager estimates that they will sell at least twice as much ice cream as frozen yogurt so he wants to ensure that he purchases enough ice cream to have at least twice as much as frozen yogurt. PROFIT per gallon of ice cream is $4.15 and PROFIT per gallon of frozen yogurt is $3.60. Finally, the manager can add additional freezer space of 10 gallons by renting the space from the neighboring restaurant for $10 per gallon. The manager would like to plan what to purchase for the next week so that he maximizes overall profit. Formulate this problem as a linear program. Make sure to clearly define you variables and label your constraints.

Answer 1

Decision variable

X₁ = Gallon of ice cream X₂ =Gallon of yoghurt

Obective function - Profit maximisation = 4.51 x₁+3.60 x₂

  Subect to = 0.93 x_{1 +} 0.75 x₂ <₌ 90

Constraints = x_{1 +} x₂ <₌ 115

x₁ >₌ 2 x₂  

  x₁ - 2x₂ >₌ 0

x₁ >₌ 0 , x₂ >₌ 0

profit maximisation = 4.51 x₁ + 3.60 x₂

subect to = 0.93 x₁ + 0.75 x₂ <₌ 80

Constraint = x₁ + x₂ <₌ 125