Jaber Group, a manufacturer of kids wear, produces four varieties of hats (silk, polyester, wool and cotton). The company sells a silk hat for $14.95, a polyester hat for $8.50, wool for $16.75 and cotton for $9.99 each. Jaber has monthly contracts with retailers to supply 75 silk, 600 polyester, 200 wool and 400 cotton hats. The company can obtain a maximum of 120 yards of silk at $25 per yard, 200 yards of polyester at $12 per yard, 80 yards of wool at $28 per yard and 125 yards of cotton at $15 per yard each month. Each hat uses material as follows: one silk hat requires 0.25 yards of silk, one polyester hat requires 0.205 yards of polyester, one wool hat requires 0.275 yards of wool and one cotton hat requires 0.22 yards of cotton. Monthly demand for their hats is as follows: 100 silk, 2,000 polyester, 250 wool and 2,000 cotton hats. It costs the company $1 in labour to produce one hat (any variety). Jaber Group wishes to know how many of each type of hat to produce to maximize its monthly profits. Setup a simplex LP model, and determine how many of each type of hats the company should produce to maximize monthly profits? Assume that the company will not produce unfinished hats