A family has some rose plants in its garden. The family wants to use a fertilizer in their garden. To prepare the fertilizer, the family needs to blend two chemicals (1 and 2). These chemicals provide the required nutrients for the roses. The prominent nutrients are, namely, nitrogen, phosphate, and potassium. A pound of  Chemical 1 provides 7 ounces of nitrogen, 6 ounces of phosphate, and 2 ounces of potassium. A pound of Chemical 2 provides 5 ounces of nitrogen, 8 ounces of phosphate, and 7 ounces of potassium. The rose plants need at least 20 ounces of nitrogen, 30 ounces of phosphate, and 10 ounces of potassium. Chemical stores sell the chemicals in pounds, not in fractions of pounds. Chemical 1 costs €5 per pound and Chemical 2 costs €6 per pound. The family wants to determine the quantity of each chemical to buy and lend to minimize cost.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.