Exercise $18-3$ Algo

Los Lobos Healthcare, a manufacturer of medical equipment and supplies, produces two types of disposable face masks: dust masks and surgical masks. The masks are produced and sold in retall boxes, with each box containing $50$ masks. The profits for each box of dust and surgical masks are $$22\mathrm{.}00$ and $$27\mathrm{.}50,$ respectively.

To manufacture the masks, Los Lobos uses the same synthetic fabric and manufacturing process. Each box of dust masks requires about $60$ square feet of the synthetic fabric and $2\mathrm{.}1$ hours of machine time. Each box of surgical masks requires $78$ square feet of the fabric and $3\mathrm{.}2$ hours of machine time. For each production cycle, Los Lobos Healthcare procures $2,000$ square feet of fabric and can operate its machines up to $80$ hours. Formulate and solve the IP model to answer the following questions.

a$.$ How many boxes of the dust and surgical masks should Los Lobos Healthcare manufacture? What is the maximum profit the company can generate?

Note: Round "maximum profit" to $1$ decimal place.

$\backslash$table$[[$Dust masks,,boxes$],[$Surgical masks,,boxes$],[$Maximum profit,,$]]$

b$.$ If Los Lobos Healthcare can increase the synthetic fabric supply to $2,200$ square feet for each production cycle, how many boxes of the dust and surgical masks should the company produce? What is the maximum profit the company can generate?

Note: Round "maximum profit" to $1$ decimal place.

$\backslash$table$[[$Dust masks,,boxes$],[$Surgical masks,,boxes$],[$Maximum profit,,$]]$

c$.$ In addition to the $2,200$ square feet of the synthetic fabric in part b$,$ Los Lobos Healthcare will also lease additional equipment to increase the machine time to $90$ hours per production cycle. With the added capacity. how many boxes of the dust and surgical masks should the company produce? What is the maximum profit the company can generate?

Note: Round "maximum profit" to $1$ decimal place.

$\backslash$table$[[$Dust masks,,boxes$],[$Surgical masks,,boxes$],[$Maximum profit,,$]]$