Product Mix Decision, Single Constraint

Norton Company produces two products $($Juno and Hera$)$ that use the same material input. Juno uses two pounds of the material for every unit produced, and Hera uses five pounds. Currently.

Norton has $16,000$ pounds of the material in inventory. All of the material is imported. For the coming year, Norton plans to import an additional $8,000$ pounds to produce $2,000$ units of Juno and $4,000$ units of Hera. The unit contribution margin is $30$ dollars for Juno and $60$ dollars for Hera. Also, assume that Norton's marketing department estimates that the company can sell a maximum of $2,000$ units of Juno and $4,000$ units of Hera.

Norton 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 $8,000$ pounds it planned to use in the coming year's production. There is no other source of the matenal.

Required:

$1.$ Compute the total contribution margin that the company would earn if i could manufacture

$2,000$ units of Juno and $4,000$ units of Hera.

$2.$Determine the optimal usage of the company's inventory of $16,000$ pounds of the material.

Compute the total contribution margin for the product mix that you recommend.