Help with linear equations word problem?

[spadeheart]

American Motor Works produces SUVs and Trucks at the same plant. Each SUV requires 4 minutes on the body assembly line, 5 minutes in the paint booth, 8 minutes on the interior installation line and 3 minutes to install the luxury trim. The factory sells SUVs to dealerships for $18665. each truck requires 3 minutes on the body assembly line, 6 minutes in the paint booth, 3 minutes on the interior assembly line and 8 minutes to apply bed-lining. The trucks sell for $13315. For one two-week pay period, American has trained labor available to operate the body line for 110 hours, the interior line for 174 hours, the paint booth for 193 hours, the bed-lining booth for 220 hours and the luxury trim station for 3510 minutes. The body line and paint both each cost $34500 per hour to run, the interior line costs $52800 per hour to run, bed-lining costs $22500 per hour to install, and luxury trim costs $69,000 per hour to install.
a. Determine the profit on each variable and an equation for the total profit this pay-period.
b. Create a resource chart and determine the constraints
c. Graph the feasible region.

 

[HallsofIvy]

What, exactly, is your difficulty? Are you not able to write out the appropriate inequalities? You are told that "Each SUV requires 4 minutes on the body assembly line". If we let "S" be the number of SUVs built then the SUVs will need 4S minute on the assembly line. You are told that "each truck requires 3 minutes on the body assembly line". Letting "T" be the number of trucks built, the trucks will need 3T minutes on the assembly line. So a total of 4S+ 3T minute will be required. You are also told that "American has trained labor available to operate the body line for 110 hours" which is 110(60)= 6600 minutes. 4S+ 3T cannot be more than 6600: \(\displaystyle 4S+ 3T\le 6600\). Do the same for "paint booth", "interior installation", and "luxury trim".

You are told that an SUV sells for $18665 but "The body line and paint both each cost $34500 per hour to run". Since an SUV requires the body line for 4 minutes= 4/60= 1/15 hour on the body line and 6 min= 6/60= 1/10 hour, there is a cost of 34500/15= $2300 for the assembly line and 34500/10= $3450 for the paint booth. That reduces the profit to 18665- 2300- 3450= $12915. Do the same with the cost of "interior installation" and "luxury trim" to determine the actual profit on each SUV.