National express carriers is interested in two attributes

Question

National Express Carriers is interested in two attributes:

Attribute 1 The average cost of delivering a letter (known to be between $1 and $5)

Attribute 2 Percentage of all letters reaching their destination on time (known to be between 70% and 100%)

a Would National's multiattribute utility function exhibit mui?

b Would National's utility function be additive?

c Assume that attributes 1 and 2 exhibit mui. Suppose National is indifferent between ($1, 70%) for certain and the following lottery:

Also assume that National is indifferent between ($5, 100%) for certain and

Find National's multiattribute utility function. Express National's multiattribute utility function in terms of u₁(x₁) and u₂(x₂).