Product Mix Decision, Single Constraint

Patz Company makes three types of stainless steel frying pans. Each of the three types of pans requires the use of a special machine that has total operating capacity of $156,050$ hours per year. Information on each of the three products is as follows:

Basic Standard Deluxe

Selling price $$12\mathrm{.}54$ $$16\mathrm{.}78$ $$31\mathrm{.}80$

Unit variable cost $$7\mathrm{.}22$ $$10\mathrm{.}74$ $$13\mathrm{.}56$

Machine hours required $0\mathrm{.}100\mathrm{.}200\mathrm{.}50$

The marketing manager has determined that the company can sell all that it can produce of each of the three products.

Required:

$1.$ How many of each product should be sold to maximize the total contribution margin? If a product should not be produced at all, enter $"0"$ for your answer.

Number of basic units: fill in the blank $1$

Number of standard units: fill in the blank $2$

Number of deluxe units: fill in the blank $3$

What is the contribution margin per machine hour for each of these products? If required, round your answers to the nearest cent.

Basic units: $fill in the blank $4$

per machine hour

Standard units: $fill in the blank $5$

per machine hour

Deluxe units: $fill in the blank $6$

per machine hour

What is the total contribution margin for this product mix?

$fill in the blank $7$

$2.$ Suppose that Patz can sell no more than $257,000$ units of each type at the prices indicated. What product mix would you recommend?

Number of basic units: fill in the blank $8$

Number of standard units: fill in the blank $9$

Number of deluxe units: fill in the blank $10$

What would be the total contribution margin?

$fill in the blank $11$

$3.$ What data analytic type$($s$)$ are being used in Requirements $1$ and $2?$ Choose from the following types: descriptive, diagnostic, predictive, and prescriptive. Explain your choices. See Exhibits $2\mathrm{.}5$ and $2\mathrm{.}6,$ for a brief review of data analytics.

In both requirements, the optimal product mix is calculated by the model; thus, the mix is what

should be

used and accordingly corresponds to the

prescriptive

type.