A Company Produces Three Different Products That All Require Processing

A company produces three different products that all require processing on the same machines. There are only 27,000 machine hours available in each year. Production information for each product is:
$$\begin{array} { | l | r | r | r | } \hline &\underline { \mathrm { A } } & \underline { \mathrm { B } } & \underline{\mathrm{c}}\\ \hline \text { Sales price per unit } & \$ 20.00 & \$ 38.00 & \$ 35.00 \\\hline \text { Variable costsper unit } & \$ 12.00 & \$ 26.00 & \$ 17.00 \\\hline \text { Machine hours necessary to produce one unit } & 2.5 & 4.0 & 4.50 \\\hline\end{array}$$ Required:
(1) Determine the preferred sales mix if there are no market constraints on any of the products.
(2) Determine the preferred sales mix if the demand is limited to 5,000 units for each product.
(3) Determine the preferred sales mix if the demand is limited to 3,000 units for each product.