Design DC circuit with 15V battery for +10V, +5V, −5V outputs at ≤1mA

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Homework Statement

Design a DC cct having a 15V battery to provide the following node voltages: +10V, +5V, and -5V with respect to a circuit ground node. Select your resistors such that the max power demand on the battery does not exceed 1mA.

The Attempt at a Solution

I made a cct with 4 series resistors. 15V source is in series with R1, which is in series with R2, which is in series with R3, which is in series with R4. Since in the question the voltage drops are all equal (5V), I selected 4 equal resistors of 4k. With this design I can node voltages of +7.5, +3.75 and -3.75 with respect to a circuit ground. (I chose the cct ground to be the node connecting R3 and R4)

For the life of me, I don't see a way to get the node voltages specified in the question. Can somebody PLEASE guide me in the right direction??

 

[Delta]

Try sketching down the outputs you want in order, starting with -5V, 0V (ground), 5V and 10V. How many gaps are there between the nodes?