A developer reviewing the design of a $20 million building faces a tradeoff between construction costs and energy consumption. The current design requires 10 million btu/year of heating and cooling power. Available modifications such as the addition of awnings, improved insulation, and solar panels could save up to 7 million btu/year, at a total additional cost of $4 million. Since the range of possibilities and the uncertainties involved with some modification technologies, the developer wants you to help her sort out her preferences. From interviews you determine that for building cost, she is indifferent between

$22.5M and ($24M, 0.5; $20M)
$23.4M and ($24M, 0.5; $22.5M)
$21.5M and ($22.5M, 0.5; $20M)

regardless of the level of energy used.

Similarly, for energy consumption in millions of btu/year, she is indifferent between

5 and (10, 0.5; 3)
3.75 and (5, 0.5; 3)
7 and (10, 0.5; 5)

regardless of the level of costs.
For combinations of costs and energy, she is indifferent between

($20M, 10) = the current plan and [($24M, 10), 0.1; ($20M, 3)]

and also indifferent between

($24M, 3) = the maximum energy conservation plan and [($24M, 10), 0.2; ($20M, 3)]

Required:
a. Solve for the implied utilities from the indifference statements above.
b. Would the developer prefer the current design or the alternative [(22.5, 7), 0.6; (22.4, 3.75)]?
c. Find K by applying the general formula and check the results from part (b).