Question $1$: $(30$ points$)$

The company Jugueton sells two electric ride$-$on cars. They buy all the components from

different suppliers and they assemble by hand the products. The ride$-$on cars are tested before

being packaged for sale. The difference between the products is that car $Y$ also has a remote$-$

control feature. The following budgeted details relate to the ride$-$on cars:

The following costs are derived from their budget this year:

During the following month there is a limitation in the number of hours allocated for

assembling and testing because of a legal union action. For assembly, they are limited to $100$

hours and for testing $50$ hours. The managers want to find out how the resources should be

distributed by product in order to maximize their profits.

Required

$1.$ Calculate the contribution per unit for each type of product $(5p).$

$2.$ Determine the objective function based on these two constraints $(2$ p$).$

$3.$ Write the equations for the two constraints $(2p)$