Solve the problem.
-A manufacturer produces two models of a gas grill.Grill A requires 0.9 hr for assembly and 0.5 hr for packaging. Grill B requires 1.2 hr for assembly and 0.8 hr for packaging. The production Information and profit for each grill are given in the table. The manufacturer has 1,152 hr of labor Available for assembly and 716 hr of labor available for packaging.

\begin{array} { l | c | c | c } & \text { Assembly } & \text { Packaging } & \text { Profit } \\\hline \text { Grill A } & 0.9 \mathrm { hr } & 0.5 \mathrm { hr } & 80 \\\text { Grill B } & 1.2 \mathrm { hr } & 0.8 \mathrm { hr } & 110\end{array}

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.
b. What is the maximum profit under these constraints?
c. If the profit on grill A units is 120 and the profit on grill B units is unchanged, how many of each Type of grill unit should the manufacturer produce to maximize profit?

A) a.

\mathrm { A } = 0 , \mathrm {~B} = 895

b. Profit

= 98,450

c. 520 units of

A

and 570 units of B

B) a.

A = 520 , B = 570

b. Profit = 57,656
c. 1,280 units of A and 0 units of B

C) a.

\mathrm { A } = 520 , \mathrm {~B} = 570

b. Profit

= 104,300

c. 1,280 units of

\mathrm { A }

and 0 units of

\mathrm { B }

\mathbf { a } . \mathrm { A } = 1,280 , \mathrm {~B} = 0

b. Profit

= 102,400

c. 1,280 units of

\mathrm { A }

and 0 units of

\mathrm { B }

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