1. Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements and unit price for each product are given in the table below. Currently, 900 labor hours, 1550 gallons of paint, and 1600 board feet of lumber are available. Product Labor Lumber Paint Price($) 1 1,5 2 3 26 2 3 3 2 28 3 1 4 2 31

Optimal tableau of the problem is: BV x1 x2 x3 x4 x5 x6 RHS z 0 0 0 17/16 41/8 151/32 16450 x2 0 1 0 1/2 0 -1/4 50 x3 0 0 1 -5/16 3/8 -3/32 150 x1 1 0 0 -1/8 -1/4 9/16 400 (x1, x2 and x3 are number of product 1, 2 and 3 to be produced; x4, x5 and x6 are the slacks of labor, paint and lumber constraints respectively.

a) (15 points) Overtime labor is available at $4 per hour. Should Productco let its workers work overtime? Briefly explain.

b) (15 points) Due to supply chain problems only 1000 gallons of paint, and 1200 board feet of lumber are available, what would be the new optimum solution?

c) (15 points) Marketing department has identified the demand for a fourth product, which would require 2 hours of labor, 3 gallons of paint, and 2 board feet of lumber. What is the minimum price of this product to be profitable?