Sleak Teak builds yard furniture using hardwoods and (in a smaller shop) handcrafted knick-knacks from the same sort of wood. The hardwood usage in the two lines of product are

Yard Furniture: Y = 2 Ty - .001Ty2
Knick-knacks: Z = 20Tz - .01 Tz2

where Y and Z are units of furniture and knick-knacks respectively. Ty and Tz are the amounts of hardwood used in Y and Z production respectively. Yard furniture can be sold at a profit (i.e., net of costs) of $100 per unit and knick-knacks can be sold at a profit of $25 per unit. Sleak Teak has 1300 units of hardwood available that can be allocated between these two lines of production.

(a) Using the Lagrangean Multiplier method, determine how should the hardwood be allocated between the two lines of product so that total profit can be maximized. Also calculate the optimal amounts of Y and Z and total profit from each product line.

(b) Using Excel Solver verify your answers to (a) above.