Posted by **Michelle** on Wednesday, May 25, 2011 at 9:12pm.

3. (i) 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 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.)