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. The supplier is also instructed that there should be no more than 70 pounds of (B) yarn.
Each contain the proportions of cotton and silk (by weight) as shown in the following table:
Cotton Silk
A 30% 60%
B 50% 10%
Material A costs $3 per pound, and B costs $2 per pound.
a. What quantities (pounds) of A and B yarns should be used to minimize the cost of this order? [ Select ] ["A - 33.33; B - 70", "A - 25; B - 45", "A - 65; B - 41.67", "A - 30; B - 72"]
b. What is the total cost? [ Select ] ["$285", "$232", "$247", "$240"]
c. Are there any unused resources? [ Select ] ["yes", "cannot determine", "no"] If so/not, what constraint and how much more should be considered ? [ Select ] ["In silk; 2 pounds", "In cotton; 3.25 pounds", "There are no unused resources", "In cotton; 10 pounds"]
d. What if it was decided to increase cotton by 3 pounds. What impact would it have on cost? [ Select ] ["$10", "$0 - because there is no shadow price", "$45", "$30"]