Fruity Ltd manufactures an orange flavoured soft drink called OrangeFiZZ by combining orange soda and orange juice. Each ounce of orange soda contains 0.5 oz of sugar and 1 mg of vitamin C. Each ounce of orange juice contains 0.25 oz of sugar and 3 mg of vitamin C. It costs Fruity 2 pence to produce an ounce of orange soda and 3 pence to produce an ounce of orange juice. Fruity’s marketing department has decided that each 10 oz bottle of OrangeFiZZ must contain at least 20 mg of vitamin C and at most 4 oz of sugar.
I have formulated this data. The variables are: $x_1$=number of ounces of orange soda in a bottle of OrangeFiZZ, $x_2$=The number of ounces of orange juice in a bottle of OrangeFiZZ
the objective function is $2x_1+3x_2$ as a minimum
the constraints are: $0.5x_1+0.25x_2\leqslant 4$ for the amount of sugar, $x_1+3x_2\leqslant 20$ for the Vitamin C, $x_1+x_2\leqslant 10$ for the 10oz in 1 bottle of OrangeFiZZ and $x_1, x_2\geqslant 0$.
I am stuck on the way I would go solve the LLP whilst also finding the optimum value of the objective function, the basic feasible optimal vector and the amounts of sugar and vitamin C required to achieve the optimum.