1a) An appliance manufacturer produces two models of microwave ovens: the super
ID: 2729368 • Letter: 1
Question
1a) An appliance manufacturer produces two models of microwave ovens: the super nuker and the Micro-1000. Both models require fabrication and assembly work. The super nuker requires 4 hours of fabrication and 2 hours of assembly. The Micro-1000 requires 2 hours of manufacturing and 6 hours of assembly. There are 800 fabrication hours and 620 hours for assembly available this week. Each super nuker contributes $45 to profit and each Micro-1000 contributes $37 to profit. What quantities of super nukers and Micro-1000's will maximize profit? How much profit will the manufacturer realize?
1b) Suppose the manufacturer introduces another model: the WAVE. This model requires 3 hours of fabrication and 3.5 hours of assembly. In addition, this model contributes $43 to profit. We would like to produce at least 30 Micro-1000's and no more than 125 Super-Nuker's. How would the profits change, assuming the conditions from the previous problem are in effect? Report the optimal quantities to give this profit as well as 1 other interesting fact.
1a) An appliance manufacturer produces two models of microwave ovens: the super nuker and the Micro-1000. Both models require fabrication and assembly work. The super nuker requires 4 hours of fabrication and 2 hours of assembly. The Micro-1000 requires 2 hours of manufacturing and 6 hours of assembly. There are 800 fabrication hours and 620 hours for assembly available this week. Each super nuker contributes $45 to profit and each Micro-1000 contributes $37 to profit. What quantities of super nukers and Micro-1000's will maximize profit? How much profit will the manufacturer realize?
1b) Suppose the manufacturer introduces another model: the WAVE. This model requires 3 hours of fabrication and 3.5 hours of assembly. In addition, this model contributes $43 to profit. We would like to produce at least 30 Micro-1000's and no more than 125 Super-Nuker's. How would the profits change, assuming the conditions from the previous problem are in effect? Report the optimal quantities to give this profit as well as 1 other interesting fact.
Explanation / Answer
1 a) Let S denotes units of Super nuker and M denotes units of Micro-1000.
Profit of supernuker is 45 and Profit of Micro-1000 is 37.
Maximize profit = 45 S + 37 M
Super nuker requires 4 hours of fabrication and Micro-1000 requires 2 hours of fabrication.
Total fabrication hours = 800 Hours
4 S + 2 M = 800 [Equation 2]
Super nuker requires 2 hours of assembly and Micro-1000 requires 6 hours of assembly.
Total assembly hours = 620 Hours
2 S + 6 M = 620 [ Equation 3]
Solving equation 2 and 3,
4 S + 2 M = 800
4 S + 12 M = 1240 [Multiply equation 3 by 2]
(-) (-) = (-) [Changing the mathematical signs both sides.]
(-) 10 M = (-) 440
M = 44
and S = [800 - 2 M] / 4
= 800 - 2 *44 / 4
= 800 - 88 / 4
= 178
Conclusion:- 178 Units of Supernukers and 44 Units of Micro-1000 will maximize profits. Total profits that manufacturer realize = 178 * 45 + 44 * 37 = 8010 + 1628 = $ 9638
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.