Decision Variables

Products

Objective Function

Profit

Constraints

LHS

RHS

Demand Constraints

$xA$

$xB$

$xC$

xD $$

$xE$

$xF$

Testing Equipment Time Constraints

T$3$

Decision Variables are Integer

Non$-$Negativity

X$\_$A $0$ X$\_$B $0$ X$\_$C $0$ X$\_$D $0$ X$\_$E $0$ X$\_$F $0$hello so i got a question and i need to use linear programming and i answered it only half can you show me how and the answer using excel for the question please.

QUESTION $1$ LINEAR PROGRAMMING

An auto part manufacturer sells six different parts to automobile companies: spot lights $($A$),$ break lights $($B$),$ headlights $($C$),$ thermostat $($D$),$ fan ditch $($E$),$ and battery $($F$).$ Demand is expected to be within $2,000,1,500,1,800,1,200,1,000$ and $1,000$ units of each of the auto parts, respectively. The table that follows summarizes the revenues and material costs for each product:

Auto Parts Produced

A B C D E F

Price per Unit $200120180200430260$

Material Cost per Unit $3525404517060$

Each of these auto parts needs to be tested before being sold. Specifically, there are three different tests the protocol requires each part passes, before completing the quality check. Appropriate testing equipment is required for each test: T$1,$ T$2$ and T$3.$ Equipment T$1$ and T$2$ are available $100$ hours per week each, while T$3$ is available only $80$ hours per week. The time $($in minutes$)$ required per device for each of the three tests is reported in the following table:

Electronic Devices Produced

A B C D E F

Test on T$1731261817$

Test on T$225321517$

Test on T$3513292$

Specialized personnel is required to operate each of the test equipment. The variable labour costs are $16$ per hour for equipment T$1,12$ per hour for T$2,$ and $20$ per hour for T$3.$

A$)$ Considering the manufacturer intends to maximize profit, write a linear program for this problem and find a solution with Excel Solver. Reflect on whether to impose a constraint on the nature of the decision variables.