Assume that the total sales value at the split$-$off point for product $1$ is $$81,000$ instead of $$189,000$ and the sales value of product $3$ is $$2,700$ instead of $$27,000.$ Assume also that, because of its relatively low sales value, the firm treats product $3$ as a by$-$product and uses the asset recognition method for accounting for by$-$products. What amount of joint cost would be allocated to the products using the sales value at split$-$off method? Required information

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The following information relates to a joint production process for three products, with a total joint production cost of $\backslash (\backslash$$ $135,000\backslash ).$ There are no separable processing costs for any of the three products.

Assume that the total sales value at the split$-$off point for product $1$ is $\backslash (\backslash$$ $81,000\backslash )$ instead of $\backslash (\backslash$$ $189,000\backslash )$ and the sales value of product $3$ is $\backslash (\backslash$$ $2,700\backslash )$ instead of $\backslash (\backslash$$ $27,000\backslash ).$ Assume also that, because of its relatively low sales value, the firm treats product $3$ as a by$-$product and uses the asset recognition method for accounting for by$-$products. What amount of joint cost would be allocated to the products using the sales value at split$-$off method?

Answer is complete but not entirely correct.