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

​1/4040

of a day and

​1/7575

of a day to paint a truck of type T1 and a car of type C1 in the paint​ shop, respectively. It takes

​1/4545

of a day to assemble either type of vehicle in the assembly shop.

A T1 truck and a C1 car yield profits of

$ 300$300

and

$ 220$220​,

​respectively, per vehicle sold.

The aim of the objective function for Green Vehicle Inc. should be to

Maximize

the objective value.

The optimum solution​ is:

Number of trucks to be produced per day​ =

nothing

​(round your response to two decimal​ places).

Answer 1

Based on the given data, we get

Total Profit = 300*T1 + 220*C1

We have to maximize this profit

Subject to Constraints:

(1/40) * T1 + (1/75)*C1 <= 1............Constraint for Time required in painting per day

15*T1 + 8*C1 <= 600

(1/45) * T1 + (1/45) * C1 <= 1..........Constraint for Time required in assembly per day

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:

Above solution in the form of formulas along with Excel Solver Extract is shown below for better understanding and reference:

The optimum solution is:

No. of trucks to be produced per day = 34.29

No. of cars to be produced per day = 10.71

Optimal Solution Value = $12,642.86

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