Question

Once you got the utility function working for David, Hilary started losing. Now, she is turning to you to help her with the tough decisions she has to make.

From her experience, she can tell how much fixing up each room Is important to her clients by listening to what they say. She knows that for her current client, opening up the main floor is really important and it has a coefficient of 50 happy point per dollar spent in that room. Fixing the kitchen gets 30 happy points per dollar spent. Bathroom 1 has 20 happy points per dollar spent and Bathroom 2 has 12 happy points per dollar spent.

She is given a budget of $70,000 to fix up the house. If she spends all the money on fixing up those 4 rooms, and decides she has to spend a minimum of $6,000 on each bathroom, $12,000 on the kitchen and $18,000 to open up the first floor

Answer 1

Let X1 be the amount (dollars) spent on the main floor

X2 be the amount (dollars) spent on kitchen

X3 be the amount (dollars) spent on bathroom 1

X4 be the amount (dollars) spent on bathroom 2

Max 50X1+30X2+20X3+12X4

s.t.

X1+X2+X3+X4 <= 70000

X3 >= 6000

X4 >= 6000

X2 >= 12000

X1 >= 18000

Solution is determined using Solver as follows:

FORMULAS:

F3 =SUMPRODUCT(B3:E3,$B$11:$E$11) copy to F5:F9

Optimal decision:

X1 = the amount (dollars) spent on the main floor = $ 46,000

X2 = the amount (dollars) spent on kitchen = $ 12,000

X3 = the amount (dollars) spent on bathroom 1 = $ 6,000

X4 = the amount (dollars) spent on bathroom 2 = $ 6,000

Total happy points = 2,852,000