Arizona Developers purchased and subdivided a tract of land that cost $$900,000$ cash into garden lots. The garden lots were divided on the following basis.

$10\%$ used for public walkways and parking

$50\%$ divided into $75$ lots selling at $$4,000$ each $($Category $1)$

$30\%$ divided into $200$ lots selling at $$3,000$ each $($Category $2)$

$10\%$ divided into $50$ lots selling at $$2,000$ each $($Category $3)$

Required

a$.$ Prepare the entry for the purchase of the lots for cash. Use the relative sales value method to allocate the total cost of $$900,000$ to the three inventory categories of lots. Assume a perpetual inventory system.

b$.$ During the final month of the year, the walkways and parking were completed $($included in the $$900,000$ cost$)$ and several sales occurred. Inventory remaining at year$-$end was: $20$ of the $$4,000$ lots; $50$ of the $$3,000$ lots; and $10$ of the $$2,000$ lots.

$(1)$ Compute the valuation of inventory at year$-$end.

$(2)$ Prepare the entry for sales and cost of goods sold for each category of lots separately. Assume cash sales.