Norton Company produces two products $($Juno and Hera$)$ that use the same material input. Juno uses two kilograms of the material for every unit produced, and Hera uses five kilograms. Currently, Norton has $16,000$ kilograms of the material in inventory. All of the material is imported. For the coming year, Norton plans to import an additional $8,000$ kilograms to produce $2,000$ units of Juno and $4,000$ units of Hera. The unit contribution margin is $$30$ for Juno and $$60$ for Hera.

Norton Company has received word that the source of the material has been shut down by embargo. Consequently, the company will not be able to import the $8,000$ kilograms it planned to use in the coming year's production. There is no other source of the material.

Required:

$1.$ Compute the total contribution margin that the company would earn if it could manufacture $2,000$ units of Juno and $4,000$ units of Hera.

$2.$ Determine the optimal usage of the company's inventory of $16,000$ kilograms of the material. Compute the total contribution margin for the product mix that you recommend