A Company Has the Following Inputs and Cost Structure They Must Also Use the Following Minimum Quantities

Essay

A company has the following inputs and cost structure.
$$\begin{array} { l l l l } \text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\\text { Ingredient A } & 4 & 2 & 4 \\\text { Ingredient B } & 2 & 2 & 1 \\\text { Ingredient C } & 1 & 5 & 3 \\\text { Ingredient D } & 6 & 8 & 7 \\\text { Cost per unit } & 0.05 & 0.017 & 0.045\end{array}$$ They must also use the following minimum quantities.
A 80, B 64, C 90, D 120
The is also a maximum of Z of 100 units.
a) Calculate how many of each product (X, Y, Z) should be produced.
b) How much is the minimized total cost?