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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: Car X Car Y Selling price/unit £260 £320 Component costs per unit £110 £130 Minutes per unit Minutes per unit Assembly time 10 20 Testing time 8 8 The following costs are derived from their budget this year: Assembly Electronic component testing £24/hour £15/hour 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 (5 p). 2. Determine the objective function based on these two constraints (2 p). 3. Write the equations for the two constraints (2 p) 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. (2.5p) (b) Draw the lines for the constraints and identify the corner points that make up the feasible region. (5p) (c) Determine the mixed of products for the comer point where both lines intercept using the substitution method. (5p) 5. Identify the mix of products that will maximize the contribution and the total contribution.(2.5p) 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

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:
Car X
Car Y
Selling price/unit
£260
£320
Component costs per unit
£110
£130
Minutes per unit
Minutes per unit
Assembly time
10
20
Testing time
8
8
The following costs are derived from their budget this year:
Assembly
Electronic component testing
£24/hour
£15/hour
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 (5 p).
2. Determine the objective function based on these two constraints (2 p).
3. Write the equations for the two constraints (2 p)
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. (2.5p)
(b) Draw the lines for the constraints and identify the corner points that make up the feasible
region. (5p)
(c) Determine the mixed of products for the comer point where both lines intercept using the
substitution method. (5p)
5. Identify the mix of products that will maximize the contribution and the total
contribution.(2.5p)
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

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