Teal Company manufactures equipment. Teal's products range from simple automated machinery to complex systems containing numerous components. Unit selling prices range from $$200,000$ to $$1,500,000$ and are quoted inclusive of installation. The installation process does not involve changes to the features of the equipment and does not require proprietary information about the equipment in order for the installed equipment to perform to specifications. Teal has the following arrangement with Winkerbean Inc.

Winkerbean purchases equipment from Teal for a price of $$1,020,000$ and contracts with Teal to install the equipment. Teal charges the same price for the equipment irrespective of whether it does the installation or not. The cost of the equipment is $$643,000.$

Winkerbean is obligated to pay Teal the $$1,020,000$ upon the delivery and installation of the equipment.

Teal delivers the equipment on June $1,2020,$ and completes the installation of the equipment on September $30,2020.$ The equipment has a useful life of $10$ years. Assume that the equipment and the installation are two distinct performance obligations which should be accounted for separately.

Assuming Teal does not have market data with which to determine the standalone selling price of the installation services. As a result, an expected cost plus margin approach is used. The cost of installation is $$36,700$; Teal prices these services with a $20\%$ margin relative to cost$.$

$($a$)$ how should the transaction price of $$1,020,000$ be allocated among the service obligations?

$($b$)$ prepare the journal entries for teal for this revenue arrangement on June $1,2020$ and September $30,2020,$ assuming Teal receives payment when installation is completed.