a manufacturer produces two models of a gas grill. grill a requires 1.2 hr for assembly and 0.5 hr for…

a manufacturer produces two models of a gas grill. grill a requires 1.2 hr for assembly and 0.5 hr for packaging. grill b requires 0.6 hr for assembly and 1 hr for packaging. the production information and profit for each grill are given in the table. the manufacturer has 600 hr of labor available for assembly and 400 hr of labor available for packaging.\n| | grill a | grill b |\n|--|--|--| \n| assembly | 1.2 hr | 0.6 hr |\n| packaging | 0.5 hr | 1 hr |\n| profit | $130 | $120 |\npart 1 of 3\n(a) determine the number of grill a units and the number of grill b units that should be produced to maximize profit assuming that all grills will be sold.\nthe manufacturer should produce 400 grill a units and 200 grill b units to maximize profit.\npart 2 of 3\n(b) what is the maximum profit under these constraints?\nthe maximum profit is $□.

a manufacturer produces two models of a gas grill. grill a requires 1.2 hr for assembly and 0.5 hr for packaging. grill b requires 0.6 hr for assembly and 1 hr for packaging. the production information and profit for each grill are given in the table. the manufacturer has 600 hr of labor available for assembly and 400 hr of labor available for packaging.\n| | grill a | grill b |\n|--|--|--| \n| assembly | 1.2 hr | 0.6 hr |\n| packaging | 0.5 hr | 1 hr |\n| profit | $130 | $120 |\npart 1 of 3\n(a) determine the number of grill a units and the number of grill b units that should be produced to maximize profit assuming that all grills will be sold.\nthe manufacturer should produce 400 grill a units and 200 grill b units to maximize profit.\npart 2 of 3\n(b) what is the maximum profit under these constraints?\nthe maximum profit is $□.

Answer

Explanation:

Step1: Define the profit - function

Let $x$ be the number of grill A units and $y$ be the number of grill B units. The profit function $P$ is $P = 130x+120y$.

Step2: Set up the constraints

For assembly time: $1.2x + 0.6y\leq600$. For packaging time: $0.5x+1y\leq400$. Also, $x\geq0,y\geq0$. We know from part (a) that $x = 400$ and $y = 200$.

Step3: Calculate the maximum profit

Substitute $x = 400$ and $y = 200$ into the profit - function $P$. $P=130\times400 + 120\times200$ $P = 52000+24000$ $P=76000$

Answer:

76000