Response to the following problem:
I ^awn fertilizer is rated according to three levels: nitrogen, phosphorus, and potassium. The nitrogen content affects the greening; the phosphorus affects the sturdiness of the root structure; and the potassium affects the disease-fighting capabilities of the plants. For example, the rating of one Scotts Turf Builder product is 27-3-4, meaning that it consists of 27% nitrogen, 3% phosphorus, and 4% potassium. Beauty Grow plans to market two lawn-fertilizing products, which it will call Beauty Green and Beauty Turf. It plans to sell a 20-pound bag of Beauty Green for $G and a 20-pound bag of Beauty Turf for $T. Lawn fertilizer is a mixture of many different compounds, but, for simplicity, let us suppose that it is a mixture of three, each of which has various amounts of nitrogen, phosphorus, and potassium. They sell for $C1, $C2, and $C3 per pound, respectively. During a production run, limited amounts of each of the three compounds are available (L1, L2, and L3, respectively), and demand for bags of each of the two lawn fertilizers (D3 and D2) is limited.
a. What are the uncontrollable inputs (i.e., the parameters) for this problem?
b. The controllable inputs (i.e., the decision variables) for this problem are the total amount (pounds) of each of the three compounds that are to be mixed into bags of Beauty Green and the total number of pounds of each of the three compounds that are to be mixed into bags of Beauty Turf. Define six decision variables for this problem. Be sure to include the units for your decision variables. (This is very important!)