Willy Wonka has engaged your consultation services to assist in the recipe formulation of a new brand of chocolate bar, weighing \(100 \mathrm{~g}\), which he plans to name "Super-choc." Each chocolate bar contains two types of chocolate, African and Belgian, with the balance consisting of sugar. Mr. Wonka has requested you to define the optimal composition of the new chocolate bar for minimum cost such that the following conditions are satisfied:

(a) Each bar should contain at most \(60 \mathrm{~g}\) of chocolate.

(b) The amount of African chocolate in each bar should not be more than \(10 \mathrm{~g}\) in excess of the amount of Belgian chocolate.

(c) The sweetness of each bar, S, should not exceed 30 units. Each gram of African chocolate reduces \(S\) by 0.3 units (relative to sugar), and each gram of Belgian chocolate raises \(S\) by one unit.

(d) The "mouth feel" of each bar, M, should be at least 40 units. Each gram of African chocolate increases M by 2.2 units, and each gram of Belgian chocolate increases \(\mathrm{M}\) by only one unit.

(e) The "lustre" of each bar, \(\mathrm{L}\), should be at least 70 units. Each gram of African chocolate increases \(\mathrm{L}\) by one unit, and each gram of Belgian chocolate increases L by 3.9 units. An example follows:

A bar of Super-choc containing \(35 \mathrm{~g}\) of African chocolate and \(25 \mathrm{~g}\) of Belgian chocolate has these properties:

\[\begin{aligned}& S=-0.3 \times 35+25=14.5 \\& M=2.2 \times 35+25=102 \\& L=35+3.9 times 25=132\end{aligned}\]

Given that the cost of Belgian chocolate is three times that of African chocolate, and the cost of sugar can be neglected, set up a suitable LP and solve it to compute the optimal mass of each of the ingredients of a bar of Super-choc.