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 1/25 of a day and ​1/75 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 $325 and $225​, respectively, per vehicle sold.

Formulate the linear program that provides the combination of T1 and C1 that maximizes yield, clearly specifying (a) variables, (b) objective function and (c) constraints.

Answer 1

Let the number of units of trucks and cars produced be T and C respectively in a given day. These are our decision variables.

The objective function, Z to maximize is the profit which is given as Z = 325T+225C

Now we have the below constraints

As the total time available for assembly is 1 day and it takes 1/45 of a day to assemble either type of vehicle in the assembly shop we have the below constraint

(1/454)T+(1/45)C 1

As the total time available for paint is 1 day and it takes 1/25 of a day and ​1/75 of a day to paint a truck of type T1 and a car of type C1 in the paint​ shop, respectively we have the below constraint

(1/25)T+(1/75)C 1

Also as we cannot produce negative quantites of trucks or cars, we have the below constraint

T 0, C 0

Also as we cannot produce fractional units of trucks and cars, we have the below constraint

T, C both are integers