Question

	Basic	Deluxe
Resin	10kg	16kg
Glass Fibre Mat	30m	50m
Profit	£50	£80

A company has been set up in Bristol to manufacture rowing dinghies. Currently, it has plans to produce a basic and deluxe version. The two dinghies are similar and both take 1.5 days to manufacture. However, the deluxe version is much stronger and the profit is higher, as can be seen in Table 14.11 Table 14.11 above. Due to safety regulations, the company is only allowed to store a limited amount of the raw material, which is 200 kg of resin and 900 m of mat. The required raw material is delivered on a daily basis. The basic dinghy is likely to be a good seller, but it is assumed that the deluxe dinghy will be limited to a maximum of 9 per day. All boats produced by the end of the day are delivered to a distribution depot as there are no storage facilities available at the plant. A. If the current labor force is 27, use the graphical method of linear programming to demonstrate that there are multiple solutions to the problem. Hence suggest a sensible mix of dinghies to produce on a daily basis and show that this results in a profit of £1000 per day. i. Set up the problem as a linear programming problem. ii. Solve using the graphical method. Show the graph of the feasible region. iii. Give the values of the decision variables and the objective function for a solution. iv. Show there are multiple solutions. Give the values of the decision variables and the objective function for two different solutions. B. What is the shadow price of the resin resource?

Answer 1

Answer: x= basic , y= deluxe.

Profit = 50x+80y. (Maximize).

y <= 9.

Graph showing feasible area:

The above problem is solved using solver:

(if we consider x and y as decimal numbers):

Profit = 1000

dv	x	y	total	rhs
value of dv	5.6	9
obj.fn.	50	80	1000
c1	10	16	200	200
c2	30	50	618	900

(if we consider x and y as integers):

Profit = 970

dv	x	y	total	rhs
value of dv	5	9
obj.fn.	50	80	970
c1	10	16	194	200
c2	30	50	600	900

We can manufacture 5 basic and 9 deluxe dinghies.

The shadow price for resin resource= 5.