Question

Green Vehicle Inc., manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/80 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/45 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $ 300 and $ 220 respectively, per vehicle sold. optimal solution? Number of trucks to be produced per days? Number of cars to be produced? Round answers to two decimal points?

Answer 1

Based on the given data,

Total Profit = 300*T1 + 220*C1

We have to maximize this objective function

Subject to constraint

(1/40)*T1 + (1/80) * C1 = 1.............Constraint for the time taken for painting

Hence, 2*T1 + C1 = 80

(1/45)*T1 + (1/45) * C1 = 1..............Constraint for the time taken in the assembly shop

Hence, T1 + C1 = 45

T1, C1 >= 0.....................................Non-negativity constraint as no. of trucks and cars cannot be negative

We solve the above LPP in Excel using Excel Solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

As seen from above, optimal solution:

T1 = 35 nos per day

C1 = 10 nos per day

Total profit = $12,700

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