1. A fabric firm has received an order for cloth specified to contain at least 45 pounds of cotton and 25 pounds of silk. The cloth can be woven out of any suitable mix of two yarns, A and B. They contain the proportions of cotton and silk (by weight) as shown in the following table: A B Cotton 30% 60% Silk 50% 10% Material A costs $3 per pound, and B costs $2 per pound. What quantities (pounds) of A and B yarns should be used to minimize the cost of this order? 2. Smitty, a clothing manufacturer that produces men's shirt and pajamas, has two primary resources available: sewing machine time (in the sewing department) and cutting-machine time (in the cutting department). Over the next month, Smitty can schedule up to 280 hours of work on sewing machines and up to 450 hours of work on cutting machines. Each shirt produced requires 1.00 hour of sewing time and 1.50 hours of cutting time. Producing each pair of pajamas requires .75 hour of sewing time and 2 hours of cutting time. The profit from each shirt is $4 and the profit from each pajama is $3. Express the Linear Programming constraints and objective mathematically. 3. Holiday Meal Turkey Ranch is considering buying two different types of turkey feed. Each feed contains, in varying proportions, some or all of the three nutritional ingredients essential for fattening turkeys. Brand Y feed costs the ranch $.02 per pound. Brand Z costs $.03 per pound. The rancher would like to determine the lowest-cost diet that meets the minimum monthly intake requirement for each nutritional ingredient. The following table contains relevant information about the composition of brand Y and brand Z feeds, as well as the minimum monthly requirement for each nutritional ingredient per turkey. Composition of each pound of feed Ingredient Brand Y Feed A 5 oz. B 4 oz. C .5 oz. Brand Z Feed 10 oz. 3 oz. 0 Cost/lb $.02 $.03 Minimum Monthly 90 oz. 48 oz. 1.5 oz.