?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

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

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

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

$4$ ?Determine the mix of products that will maximize profits for the business, using a graphical

linear programming solution:

$($a$)$ ?Solve the equations to calculate the points where both lines intercept. $(2\mathrm{.}5$p$)$

$($b$)$ ?Draw the lines for the constraints and identify the comer points that make up the feasible

region. $(5$p$)$

$($c$)$ ?Determine the mixed of products for the comer point where both lines intercept using the

substitution method. $(5$p$)$

Identify the mix of products that will maximize the contribution and the total

contribution.$(2\mathrm{.}5$p$)$

The manager wants to consider the maximum sales that they can achieve for each product.

They can sell up to $200$ ?items of $x$ ?and $220$ ?items of $Y.$ ?Reassess the feasible region and determine whether the mix of products that maximize contribution has changed. Also update the graph. $(6$p$)$