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:

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.
2. Determine the objective function based on these two constraints.
3. Write the equations for the two constraints.
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.
(b) Draw the lines for the constraints and identify the corner points that make up the feasible region.
(c) Determine the mixed of products for the corner point where both lines intercept using the substitution method.
5. Identify the mix of products that will maximize the contribution and the total contribution.
6. 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.

Transcribed Image Text:

Selling price/unit Component costs per unit Assembly time Testing time Car X 260 110 Minutes per unit 10 8 The following costs are derived from their budget this year: Assembly Electronic component testing 24/hour 15/hour Car Y 320 130 Minutes per unit 20 8