The state highway department of the state of Michigan, through the state highway commissioner, is hereby authorized to make surveys, prepare plans and specifications and take charge of the construction, including the letting of contracts and the paying out of all costs of preliminary work and construction, of roads located in part or in whole within the limits of a United States forest within this state: Provided, however, That before proceeding with any work the state highway commissioner shall, and is hereby authorized to, enter into a contract with the United States government relative to the construction of said road, said contract to provide that the state of Michigan shall be reimbursed by the United States government to the extent of 50 per cent of the total amount of funds expended by the state of Michigan and the United States government on such forest road: Provided further, That in no case shall the amount of state funds used for this purpose exceed 100,000 dollars in any 1 year.