Sleak Teak builds yard furniture, using domestic hardwoods and handcrafted knick-knacks from the same sorts of wood. Although hardwoods were readily available in the past, recently they have been much more difficult to obtain. Consultation with the plant managers of the two lines has resulted in the following production functions for hardwood usage in the two products:

Yard furniture Y = 2Ty - .001Ty²

Knick knack K = 20Tk - .01Tk²

Where Y = units of furniture K = units of knick-knacks, Ty = teak used in yard furniture and Tk = teak used in knick-knacks.

Yard furniture can be sold at a profit of $150 per unit, and knick-knacks can be sold at a profit of $75 each.Sleak Teak has 1,300 units of teak available. Calculate how many units of teak should be allocated to each product.Explain your results.