3. (i) Sleak Teak builds yard furniture using hardwoods and (in a smaller shop)

Question

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 Tz
2
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.
(Show your work.)