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.
$$\begin{array} { l l l l } \text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\\text { Ingredient A } & 3 & 2 & 4 \\\text { Ingredient B } & 2 & 3 & 1 \\\text { Ingredient C } & 1 & 0 & 2 \\\text { Ingredient D } & 6 & 8 & 4 \\\text { Cost per unit } & 0.00125 & 0.0025 & 0.015625\end{array}$$ They must also use the following minimum quantities.
A 120, B 80, C 40, D 240
The is also a maximum of Z of 80 units.
a) Calculate how many of each product (X, Y, Z) should be produced.
b) How much is the minimized total cost?