Said contract shall provide that all engineering with respect to such highways be performed by, and that all construction including the award of contracts therefor be under the supervision of, and in accordance with the plans and specifications therefor prepared by, the board of county road commissioners. The cost of engineering and supervision shall be deemed a part of the cost of the highway. Said contract shall provide that all or part of the cost of the highway improvement be allocated to the township as the township and the board of county road commissioners may agree, and shall approve the plans, specifications and estimates of cost of the highway improvement. Said contract may be executed by the township board after a majority of the legal voters of such township, voting upon said proposition, at a township meeting, a general election or a special election called by the township board for that purpose, shall vote in favor thereof, and by the board of county road commissioners after approval thereof by a resolution adopted by a majority vote of the members of said board. The contract shall be executed on behalf of the township by the supervisor and on behalf of the county road commissioners by the chairman of said board. The execution of said contract by the board of county road commissioners shall not require the approval of the board of supervisors.