On August $15,2022,$ Didgeridoo consigned $500$ electronic play systems, costing $$100$ each, to Toys RU Company. The cost of shipping the play systems amounted to $$1,250$ and was paid by Didgeridoo. On December $31,2022,$ an account sales summary was received from the consignee, reporting that $420$ play systems had been sold for $$160$ each. Remittance was made by the consignee for the amount due, after deducting a $20\%$ commission. Calculate the following at December $31,2022.$Required$1.$ The inventory value of the units unsold in the hands of the consignee$2.$ The profit for the consignor for the units sold$3.$ The amount of cash that will be remitted by the consignee.